{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Python for Finance"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Analyze Big Financial Data**\n",
    "\n",
    "O'Reilly (2014)\n",
    "\n",
    "Yves Hilpisch"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Mathematical Tools"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from pylab import plt\n",
    "plt.style.use('seaborn')\n",
    "import matplotlib as mpl\n",
    "mpl.rcParams['font.family'] = 'serif'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Approximation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "uuid": "460b709e-eed1-48e4-b3ad-d07377ea5de6"
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Convex Optimization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "uuid": "a09a918e-760c-4e9c-95b8-fe3b568dacdb"
   },
   "outputs": [],
   "source": [
    "def fm(p):\n",
    "    x, y = p\n",
    "    return (np.sin(x) + 0.05 * x ** 2\n",
    "          + np.sin(y) + 0.05 * y ** 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "uuid": "1f4a147b-d9d2-42d5-8553-dd95d75d8251"
   },
   "outputs": [],
   "source": [
    "x = np.linspace(-10, 10, 50)\n",
    "y = np.linspace(-10, 10, 50)\n",
    "X, Y = np.meshgrid(x, y)\n",
    "Z = fm((X, Y))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "uuid": "b3a1d3b7-25eb-4ac8-81ed-ad740fd1a297"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.colorbar.Colorbar at 0x1c1ba760f0>"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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MXt1mGuHLZFxc1yGKYiqV+v47DJ1vol0mRkpJLpdBCEGlUj/ynsGito1QifUk\nz15A7SPOtg3xmQtw9eWR28hGBeveB1HXXkdefAinL+3KKt8hKq5jlfvWpRtVWLsXbl/F2rlJ6eVP\no9//Z7rBS6PuyUkI4DopDRFGCVOaO9y2bVy3vwWjJIribhvNjjv8pInodGma88nOOIlI6/Tdh7tC\nnGfRoGISl3F/relWK5jqITG9W/tgO3XWvhuNoL3GPKOc5QmQfSJpZ6zxru3iClJodMZlv5HafoaW\nlGSKWVCtgfcEetgHsnmduC3a+o3nif0S3nu+aaBSVv/D/6QYOKfREouiiChKb8HY7w6PY4WUAtd1\nDtT7+qAskjgbekjn9Hm7TrU4pzWomCYKOtlv/1lqUj0pqU3ccWF7njNlIfppm1iMpzNxiKLe2nc2\nO2lnm+nGNhS1XtnojUuHROvnUXdS+jMDYuUMAJYOiUtriN2N1O0gsZCtx74GRw17SKz6LuHyPdjb\n13vH1grZrBD7RaxGGfniH1Bz80T3vGOgj3J/d6DOZz3etXq6WERrdDA6vOcO9/0MmYzX/swmcYcf\nbKyqUUdXK6haFd1oIEpL2OcvTG3JGnE+HMZyPkGMjsKeT/5wYom6tFrBQK3p6VOwZhsQJoQgmx2c\nOPS/dxRj24usDKY9ydWzI8VZ9lUkEqtnYIw4A7jr63A7ffnCapZRfh7Zl74logBhuyjbQ0Qt3OuX\nseIWrQtP0Gr3Uu7geR7FYnbAtRqGEWFll/jmFfTObWR1G9koo7wcqrBKlF8jWr8PbHfsuBebo0/N\nmoY4VoRhhG1b7OwkzU2Sjk7OkDu800bzoNHhrVdfZutf/QqNL34etEaeOU9UqaJ2thHZLM6Dj+C+\n4zG8J9+L++g7EPJgFp2Uk7fiFEK009AMlnP67sOpE+f9XNiJKE/+kBnVw7jnwlZUKrWU1KNpA8mm\ntZyH9/E8h0zGHdmk4lhm7HGIqO0OvGTbmmiEeWZ5FrQd2pZFepvINqq4ihdViErrWLvDec8ybBFn\nCmjbRUQ90ZXNKlHpLHgZ3MY2XP0y7q1XaT74PsLVXo3uOI5QSrO7vYtV3cTZuYGzcxMZNLFaVfBy\nEAVQ28GqbqGqW9juNcTrn6Nx6RuJ1u4fGtOs1w7v9pKYe48ZRXG7q1Pv/Z473KNYTCZ//W00+93h\nwWsvU//N/xfZqKE12I88Bq6Hqjew/DzC84hv3SJ44VmCF56l+m/+BSKXx//6b8Q+fwH77DmsM+ex\nz5xFuMMTNCEgjk/IB7aACGM5Lz77rS3PypLtt0QbjSZhmO4mO07L2bIk2WwGrWedszzdhKMzNikF\nfmMXtWeCJIngzMXhLlVuBinrvd5mAAAgAElEQVTi7jklMXrtHsSdt9JPtLwOxIhsHlLEGcBqVojy\nq8jd2wit0JZDvHweO6hAqAgL69iVO1itKrmvforYy6HdLMrJoP0CceUOpZ07xJlC8lp9F9EoJwVO\n6om1pqUFZx9ECgG33wQg9+xvE59/lPqjH0DN1Yo+OSUx59OgYvwxRxdLsXEcZ8AdvvHvf53Gp58i\nfO1ldKuFde4eolZIfHPQyyN8H/ueiwjLIrx1A1ko0vjs0+hq8n2wVtdZ+Zs/gnPvnmYsdCYTRxuQ\neZqQo+r3nmBOnTjvxzQRjiqM0I7d3c/zXDIZ50DtEqcvXjJtJGayT6dJRaPRIghG5yz3n+ug1st0\nEweNELJnxb/5dqq8WysrxHvFefVcInB9yNISpIizRmC3v9VWq0K4dhF7I712t13dJFq5B6IAS2rc\nVjvNKoqRlTvEmSLadkFFiDhE1suonEyscQmRX0QETZydm0PHjgtroCKsduGTOLeEUArZKGPdeIVi\nbRv7T34PERZBEJ2QNcd5ubXnMZGY/H4m0eFBt9NadOcWjX/zq4SvXkY4Dt6Fe7FKS1RfeIm4Mpxv\nrxsNwtdeBtfFffgdxBu3sdbOIO+9iLV6huJ3/wWs5ZWZjdfQw7i1TwD7CcdU4lyrQ9ZDiKSHsVKT\nWaJHle3QSb8qlXLtJhq1hXFtCiFwXbvt/q9jb10nba7rWDGxtBILtI0sloa2swiJnAwiHJwc6ZVz\nWPTta4GWEjFqPVFKRL6IDuoQDUZ2W83kAawRRPk1rGAbd/s6cXYJnStAECZriq6Pth2Um0VLC2U5\nOFvXBiYfVm0HLSTh0jmcnZvo8gaNT/0r4j/27The0oJzZaVEFEXdNdBxqVzHwUmynA8j+Fpr6v/P\nPyV68Suoyi7Ua2hA3f8IzS99ASEkmYv3Yi+vgIbmm28SlZMlGue+B4grZYKXngdABgH57/0+sh/4\n8PjRTinOJpUqQUwVdLvYnDpx3o9prD4hJVYrwM751GrNsdWzhs83nQt41Br3KDr1ugGq1cZUqVGT\nPBsmeSj4vofnOYRhTK3WAKUG0qj6kSg4dx9cf6P3mp+BPQlUUoA+exHx1iuDBygtAb3PxwobxOce\nRFx/behccWENO6ojohpaSKKl88jqBrKvS1WUXQItEFoRF1ahWUU7HuLmFZz++xFEyKBBtHwPbuU2\n0eq9WNs3EH2TDKEV9s5NouIZ7PJt7M23iJ99ispjH8JxbCqVpLiK4zjdTmVCiG7O9d510HHMT/Dm\nweyPO+31x9Vd6v/wxwlv3YT+lK318wRXriR/aEV0+ybR7bbHREgyDz6IffYculYjtiRhHJF5+FHW\n/spfR+fy+0aHG8v5cBjL+VQwmeXseQ6Zi2fZee5lnFJhImGG2TajGEWvXneAbVtTWFuTB8kd5EHS\nn7ZVr7ew7eQHJKobA6K1F2tpmbhPnEctJ9m+Q9yuBtbbVg9dhgyqUFobiPBWjocUcXdfoRV2NXlf\ne1mU5RJ7eezaFrLPOo/8ItZ2ekR5uHQep3IbAKd8mzhbRCGxqpvdbQRgVTaJcsvYtW28619FZUuw\n8qHkGG0B7vS2l1K2a1DbqWlBo3soz0vw5lV16/jd2mpni9pP/TDR9mAVOQ3oSEHQSt9RK/A8ml9+\npjsjyLz7vZz9Wz+G63k4jo1lWURRNJDO1f87NeJ8OMSBWpOeLO46cU6+//t/kJ0GEB0Xdn1rl9JU\ngV3zW3PuNalQ3Zxl3580Z3n2E4hOnW7b7qVtua5N575bu7fG7u/IkNhxIQwgv4QU6ZMNi5ho/SLi\ndrKuq3JLOHpYqISK0b6PauWQ7dKfqnQGp7U7tC2AiEOUl8fZuT7wTdGAaNYHJgMdlONj1wcrnFmt\npDRonF/Gqm73jq9jZKtO7OYQUuKVb6Cr28BwgJhSilYrGEjlGqyS1SuU0l8spTfixWcertmkJOjB\nt1cbN6n/b393SJgBrPseJnhlTFW6tTPEN97uCrN15hyF//q/p9kKabbC9nh60eGZjEehkANEV6yn\nq4Vw+gRpWkxA2Clgv7KYoxpAOGdWqL/6JpxZn+Ks04jz+Jzljvg1GoNNKo6uD3S669B1k9SUIEjW\nvNOQ+4izRCHO34+++gpiefz9lsUC3G6PqbQ6cjsRNGB5HX2rhbZd7FZl5LaJxbw99KlF2RWcvuIl\nA/sUlnHKt4fPq2KkilBeDtnq3Q8RB0l0uA6QcRN9+Y/g0Q+NvtD+caRUyXLdJMo4l/NxHBuldPt7\nkmn3UJ5FoZT5BITN57sq2LsUMgp14yrhL/0DgjvD5WM1EJdHf1cgycGPNtqfvRAU/9u/NpCXD+nR\n4R2vSGJZS5aXSygV9020Bj9nw2iM5XwC2O93Pm4ttxNJHAQhu7uDgUbehXNUP/U5MhOK86xrZLuu\ng++7Y8VvUqaz7gdd4Z01byFE6pp3d7Kh9cj15n6sQoEIEPnC2O0cEdEqriLLm1gZDwhHbmu1qkTn\n7kcHLazW6O5WWlhDbneNwKoNW1UAsZfDrowuitLNq45DRBQQF9cRGR9XNQmzK8jaBpTvYG9cIVy6\nOPZ6U8erNa1WSKvVu3bXdSiVCjiOTTabwbL21qAOJ06tm0/K0+TFNw5+3P0PrCq7xP/XT9HaThFg\nIRKr+eXLI/e3LlwkevP17t/e+96Pc/9DBxpjv1fE9zNsbm73CbaD72f2dYfPi1/5lX/GjRs3WFpa\n4tq1q/zwD/8InpeZ+3mnxVjOp4A0i9SyEvdwkg/cSK0UpDWoeh2t1JFEBu4VzE6TChgf8DVtedLD\n0EktazaDAYFIpVlBZUtYu+NT0GwREPs5rIwL7GP1rZ1FV7axxf5WhgzrxKV1opqFXdseej/yS9jV\nQQsqzpaIc8tIFaFRyKiFsCwi4aK1RscKays9XauD1awQFVbRjosdNxEqcVPbjR1ix8cKG7hvP08z\nfzZJ3zokcRyjtaZcTqqgDdegzretucFgs+Ph+LpHxf/0f0a1AqJ6C+f8PXgXziFrZQhb0GqiSh7+\nk4+i/QJRGBPf2aD11tu989h9YYFCkPv275pyvMkkpVcspdW9jk752I47/OMf/zif/OQnuXTpcR5/\n/Ekef/wJiikZDdOyubnBL//yx/jEJ34XKSU/9EN/jU996pN85CPfNrNzzBoTEHYK6Be9SXoYA5S+\n7knu/P4zLH34jx/FULv4ftLdqtEIBtxi6UxXAW2agie2LclkOpOa/VLLknHJ2iYqW9h33Vmise99\nEEvubyU4MiZYvxd5gGuOs0tYYR3tOgT5h7C3byCDRm8DpVCuT5xfToqfqAgZNUEFSfWv7oFCbJpJ\noRHLIjz/MPbtNxHxmD7Yfg7cDKLaCywSWqFtD8IGIgrI3HiBxsX37nsd+zP4gY6qQZ2UtLRTrbQg\nGCxpOZ9KXsdXrzv697+K2N0itj2KTzyatCy9+Wb3fZ0rom9eA60R23dwAAfIPPEQKr9EGGjCt98C\nIUErvPd9PXZKgZGDjTfdva81Q+7wr//6D+L7OZ5//nn++T//GJcvf5X19XX+0T/6BZaXl6c6fz+Z\nTAbHcajVahQKBRqNBg8+eDBvwHFhUqlOAR1x7rmwD9rDGHKP3M+VX/t3E4vzNOvAiftdUCzmBppU\n7L/fdAVCJl0XFwKy2cyBJjX94xK1LTQaLe1uu8hR2KvLiGi8hQ1JWpU8dy/U9neXI62kdChgB1XI\nFYjzS2jLRlkZrKCKiF1sIggSMY5tD7ueHjwW+yXs5i5Oq4xaPUcchNg7wxOPcPUitmqigxBlu8i+\nsqF2swzFdSjfwd26SrD6AHH28A/Z/SZoe1syCtEJNnPaVtpgSct5dWM6jsIm6srL6C9+Bnt5GXd7\nO72X+NIabKUsV5S3kOUt/AfeQcaP4YE1KJSwvuPPTTfSCScouVyOD3zgg3zjN34YKR3iOObmzRuU\nSrOxnnO5PN///X+VH/3RH2Z1dY319TNcuDD5cstRIu3FF+dLly79DeABYAN4FPhLly9fbozafvGv\naMZIKdtF8G0qlUbXfXQQOg+nqDJZP+hJBbNj0Uspqdeb1OvNCR6M8+3xatsWxWIOgFqtMVnOd9BA\nBLUkkrZ0Zv8d8iWUmz3QseNCCWWPj1RXTgYZDf8WhI4TVzUKGQ83rtRynJu597nIqIUlNdHS2cGx\nZZewaQugion9lHX0Zi2ZsACZm18dex0HYbrOa0kqV63WYGenwp07W2xu7tBstpAyKQXrug6rq0sU\nizkyGQ/LOvwj5KgLm6iwhfrXv4C/voI1Zq1S7w4ve3SxLPStdoW6OALbxbowXDP9YGM9nEfCsiwu\nXLh3yojvYV555TK/+qu/zE/91D/kb//tH6NUWuJjH/uFmRx7Xggpj/3fOC5dunQO+GHgr1y+fPlH\ngRzwneP2OXXiPOo73qmF7fsuSmmq1fS15f2OvfIt38Dmbzw16ag4qGXqeQ7FYpY4jlFKTxxlO81v\n/CCTByEEuVymbS03UUpPfK64r861yuT2397LExX3F3GNQEuLYPme8cfLlkZOXDQgWyO6WI14XVku\nVnMwkEigsWxJnO1ZMSo3KMZ2Y5fI32PlhE3iXGItO5XbWLVNFgGlFM1mQKVSo1Kp02oFlMvVdjtU\nl5WVEmfOrLC8XCSX83FdZ6LJ4XH0Rxb/+v/AL7hYliCqp3tm9NIaenP00os4/wC0evta755+qWv6\nezCfSfidO3coFIrY7Tq4q6trBMHYbuvHjrStY/+3D3UgAIrtv/PAC2Ov6fC3ZfFx3UTwtIZKpT71\ncbTW5J54lOozz0243/7iZ1mSQiHbtujrNJvhkTXM2G/y0Ll/ST51baq0HK1BlXsuQo1CO+Mt3ch2\nCV1/X6en8guJNe44xJn8mC1HHyl288gUN3ts+8gw3fOk/AIi5ZhCRYh8EeX6RPkVbDXsnREo9J52\nf1Z9FyWTAKNZWM/zIimS0mR3t8KdO9tsbGxTrzcRQpDPZ1lfX2ZtbYliMd9N+TtqRlrOf/AJ3Mpt\npJQoQNVGeMGyxfTXuyfY07TlyfdPNU5YvAIk73//N/Dggw/zsz/7M3zsY7/IV7/6It/7vf/lcQ9r\nPJ2OR8f5bwyXL18uA38D+LVLly59DHgLeHXcPqd6zbm/K1MnwjnpgTrtEZPmDfZyiebV62TuG2+p\ndfcak6okBGQySZOK/vXb5POeZqCTrx+PEvRx6VETp19FLVSlr1KWgLh4BnszPcpZWzYRAqRA5Vaw\nailrgp1x5pfaxxTEy/dg3UgpGOFmsFJc1t3xjHhdj+vHO6bKmYyaxCtnIVaghq0zGTaI8qs4fT2t\nhYqIcivI6gZOdQO7ukGUXxt9/jHMYy13lOCpdr/rwUIpw/2T+1sxdlK55idMKdf/2rPIFz5L5yON\n5OjJod4d/X0j48PNXtMVcfFhxPJ0nxMsnjhblsUP/uDfOu5hTMSip1JdunTpa0jE+WsvX74cXbp0\n6aeBvwP8zVH7nEpxFoJ2FPZwV6bpuz31RGzlo9/MnX/577j41/6rQ40zyUH1UptUTPtbnb7a1+BO\n/SVBW60Q0awiWzW0EOjCFIVYdm4kZQ77x+r5IzdX2eXuhUT58eLc0r0fZiwFunQGsbunIEhuCcIR\nLkwhsUYUJRllNWPZI93d/cSlNazt9NaWslUZCoyzG7soy0XGAZmbX6X6yAf3PccojrOZxKj+ya7r\nkM1mcJw8SmniOG7HgdgzLbiRKnif+v9wrN5rYT093kRnC+it4YIy3WOfvReu9Wq1y3dPbzWPHOs+\nHOY5dhpZdHEGLgBbly9f7nzJbwBjQ/tPnTgLAcVirlukY5YPqM4PIv81T3D1f/rH6P/hLx3oBzKc\nszy+YMchR8nklnOvUIplJfnUcay7EeLWxhWcN55BaIXycuhMAf3I14J3wOhQrWDn7ZQ34qHKWd13\n+tyKoe3iSRtGRHdra/Br3Mgu4Zc3EP2TAdsZKc6xm8NpDBcYUdJGNkcIcG4JkZInPXDcTAERB0Re\nDjvlGqWKiHLLe6znuGs927VN7PLtA627HwWHSXtK759sdd3epVK+L5Ur7HbmmjQuZORYv/L7uDLq\npszHlptMGNNYWoPtMWv+A2MSyMe+Zqox9sa6WJbzSeQEVAj7TeCjbYt5B3gX8APjdjh14qw1B047\nmubYQiSRgf6lh6g+8xyFP/buA+8HwxbpvMY4DZ0e0P3udevWK7hvfqm7jWzViO0M8XOfRN7/blje\nP0JVVDYQUbpLWRXXkXdSxLk/SlsIouI6dsrDVDmZocgJIQWt9Qfxbr/WtfV0MDJjAdtKn3UrO4PF\nCHG2xv90NKBFkq8d51ZSxRmSntPKspF9+dF2fSdpvJEpQFgFFkOcZ03SwCPEtm12dsp7CqV4FIt5\nQHdLWXZSug7CgOBpjf3y5xF9DUKi7BKJ8TKMjsb8LqWEjd5+4ty9iMLSgcZ0oLEapkIsuOV8+fLl\nGPjvJtnn1Ikz0F7LGv3+tPWn+y3gtf/0T3H7137jQOIMGiktikWPOJ4kZ/lo6mRLKXFdmyAIB7wN\nollF7qY8wCwLQo188yvYjTrR+cdGzwi0RqRazQnKcVJf1+5g+lLoF1PFOc6kB+5oxyZYvQ9v8yo6\nU0jSXUbRSg8SHFvUZITY9o9Ltms7W1GToHgWtzwc/StURJRdQvaX/xSC1vIFtCWxogZxUEO7+0e3\nDxx3Di7P+eQk946Zbl3LboUs389hWTZxfJCe132lZV/6I6w9ecxxPX2ypoVA3x5hUQP2uXuJ+9eb\nH3nnwS5zDIsWrX0SOY0u/lMpzvsxixKX+fc9yZW/8zOoZguZGR1YIoTAti2EkNTrDcJwFg0IRjPJ\nWlQnvcy2LYIgor5nDc6+/gKyUUZbLqIvmErWd5PKH4B1+1WUJVFnHgWREvy/8zbaShdgSKKWVXYJ\nWe9zK3s51J5jxdJCOcOR07E7ut6vyvgEpXNJkZIRxUyU7WKNsKqtEQKsHB85QtC74/JyyL6yo0LK\nxE2e4pq3mhW07SKigKBwhsjP9yJAtcKubRBOKM6QXnHqsMy+tvb4Y+4tlAJ0a0+P63ndPW4c4bzw\n9MAxlbTQt9MbmLB6Dt5+M/09QOxpaCEfede+17gf09QXTwJbT58gTcsJWHOemLsilWovs2jjKC2L\n5W/5AFu//ZmR23dSkDrRrJMK82Fc1PvRy6dWNBoBey0iWb6NVb6VrDPnBqtViagFfmKxCjSyXsa6\n/jwEewSruoEo39r3IlR+ZeDvKJdSHUsIotLZoZe1PVr4k2OVEvfwqHPb6eIe2xl0FCS51oV14uIZ\ntJe42q3c+DSbZNV/8H4KFRGWzqduL3QMpXWaaw8QZ/OJLqPR7bHJoIoYFZh2pMzjyzi5NZ6kcnUK\npWyzsbFDo9FEyk4qV/J9KhbzZC9/BsqD8QRxdilpR5rGmMkegC73VYrzMoiLD0809jSkNG7tQyPl\n8f+bMXep5Ty9OPdX4Vn7jm/hyk/8HGvf/icHtuukcEHSpMJxprvNvXFOWvZz9Belv4FGp8lHf6/l\nDvZAnu2w21Cgu6OSrSpKBVjXvoTOraIyRWhVoR1MpcMmyvaQ0Yjo2D2z3tQKWkDoZXGE7AZ6aSHQ\nQoyXDAH17DJetoSzfR0rHJxAiL7gHo0g9otEXoHI9ZFRY/B7kisl91dY+K0ajLC4VaaASLlnMm4R\nOxmsPYFpWliEfpE4jpB96VkiaqKRCBRW7Q7R0nR1m2dFYo0uXm3tvT2vhYD19VWinTuIK8P54qr9\n2BPr9+CeP4NFhCRp7RlnSsRL7yUMIa5WiW++Dc3kOyPyReI7fevNDz2OGBGvMAlCMHGHMMMgcgaf\nw6JxKsX5YBWvDn/czKMPoxt1gtubuGeSXsKdoKr+JhW2PV4wj4pOMFpaA43+6xL13QE3s2hWUG4W\n2WcZ68oW2skkpS+bFWLvbFJ8o7aJVvFAZLQAtFeAEeIMClVY6667xk56ipUWgqh0DmcncUkqr7Dv\nJEtbyZJDC0lr6QJO1MSKWkkAlopAWDRLF4htl1hY3ahPIdPdhkIIIsulunIfbm0HtzK8jmzliqiU\noCKBJiqsD3Sw0kBz5V60UmgnC30pXUIrYieLFdaRrQoiaiVNMg7ALETvKJjnOrb44m8RbwzXW7dc\nB/9r34fV2oG4d7+1ZWNVNrG1whNAAVThAqGdJ2gpBJLw1Reh/dnOwqUNyT2YJirduLV7LHpA2DSc\nSnHej2kaPbT3HNhPCMHqRz/M1m/8Dhf/m+/B9zOpTSqmdU9PY+Gnncu2k5aYSYWv4WC0vQ9xa3Nw\nzU2QpDb1i7NQcRJo1U5B6i+YJFQ09LjVevzDJ86WkJUNtO2ixtRrDrOlrjjH3v7rsMrqCywTgtDx\nCTviLy2svglD/22To6LLpQM6RgOt3BKRl8PfvDKQttWK1Mj1IituDUx0wsLZXipYHKCERPYdS0Yt\nNCIpC1q7Q1S6d99rHr6a2TAvMZj9OrYguvIiVnWLKBycJOlH3oW//RakzBNlaR11a7AojgS8qIpn\nAWfvQ9v3oawMkXAI3/HkzMZr3NqH4wSkUk3M8Ztzx8D0bu1h4Vv91g9T+fRnyWS8MU0qpp0MTCPq\nvXMJAdmsRy6XodEIqNVGNdDoG5+KUotmiBSrdyBIrLHbPbZoVYdKU4qohRhTT1tLgRYyWX8ec9FK\nSuJcsqao9in/CQwFlg2MacTXXwuZrAOnvbcnuC22HRqr93cnI1raI/dNNtDoTmMMaRH1ufCFVihn\nsNGH0DGqPZmQzd0x3ofUk02w7QGP2Pf9EUEdZ/tN8m88Tf6NPyR39Rn8t7+CXRldwGMvc2lDiSZ+\n9lNEO731YQ2IR9+F7Y/+zoR6/I9N1HaQQmCrFq5nHTqFqntcI86HRljWsf+bNXepOM/GkvU8h9XH\nL2Hns2x8/pmRNacnPt/2TcS1l4jffhXi6YLIHMemWMyhNezu1sbmh/aPz9q+ntrKUQYN1N5mDdXt\nrljJsIlou5AFINLcr2MCs4TQqOI6sb9PTWMgKCSlEtU+ucaQtlq+/7tijKDvnXQAxLZLczlpqRdl\nCvt+1qpZJXJzhIUzDAXi6XjoHIn1nNxX+yBtMeeMbFXJ3HgBb+NVnOpGEv2MRrYqOPUtsjdfIHvt\ni8hmetW1eeO+/EeIOEB3vvNCIN/xJBkrQI+rQtYaE3SXLUK9dz3yngfJZNyZLFdNJ86nz1I8FMcd\nDGYCwg7Gft/zw1nOYqBmd6VSZ/mjH2brtz/N+ceeONz54hj53KeQlz8LrkcUNGH9InzgO+EAXZwg\nEVnbtrAsOV31sUZ632IA5WWRfe8LNMrNItqv9buzZdQakr44SKy+UV9j5ReIvP1bRMaWnURg73NL\ntRz/9RYjcp/Tgrm6jKinHXlZgsJZkBLB+AmVAOL8KpHlDF+CihCZPDTKve11DF4eWlVkcxeRW993\n7Xkea85CCNTOTZydt7CCGlYwmGoWO1m0ENhBDbu5i3/zBYLSBcLl0b2AZ241xhHOndfRWqOqSUCi\nePQJMrLdsrNeTt1NSwtZHl0VLM4WsPsmG/rs/ak9r4MgJIqiie69sZwPzzws1+PmVIrzfmidpC9M\nsWc7XcMfqKJV/I8+zOZv/Ad0vYbITp6PCoBSWJ/6OPLm68mfhQuIzbfgzjXs3/0Y0Td9NxRWxh7C\n8xwyGQ+tk7XlA19VZ/IQBagxrlDZqibR0QOuzZ61Ies7RH4xSQUK62g3P2CF6yhAZIrQHPGAtCTK\ndtnXHSsErdX7ESndnvpR1hgBExKh0teV0zwH0HaRj3gPoJkt4cQBdrj/vY/tDEraWCnXEIcBAjFY\nBCVqQnvt2Q92EKUHukU40p/rM7aslELffBVZvoNV3Uw9eicSPsoUUUJiqRCv/BZShbRWHpxfXmAf\nmTeeSaKumy1QCnH+IhmZrDvH0kZU013ucW4FqzW6+MjesdcL59A7iVh3ivg4jkOhkMO27W71s07+\n9bhJshHnw3Ma15zvUnGe3HJ23aSkIAjK5erAA1FmfLyHHqT5zB/gf/gjU51PfuWprjADiL6azqK2\ni/X8p4nf/+2p7pN+S75eb5LJjM/9HUl9G6IWsV/CSrGgRRwmHaKqPQtDNsrEuaXErR2HYLvQXot2\nXI+oOShm4yy+OFMk9gpYrXTx7qeVKeE2t1KLenRQYyxnIdJn2hoxsJY+8J7ljRRuAKRNxV1iKbyy\nrzS23Byx5ZFtDLuphY6TimBBX+nQOOpGbseVDZzl8+Tzha4QBEGYUjFrRg/8oIFTvQVRDcIGKlNA\nC4mWFnZjF9HnTVC2h7adxHNiOVhRnOyrFa3Vh4dEbtpI5TREvYy38UYyjkYLkc3iFrN07kNsZUav\n4+2TLy/7LG6VLaJzff262z2vm83e96ZThtTzeoVSOpZ1p1BKN0bDiPPhMZbzaeHgAVr9TSpqtSa5\nXCbVUln9s9/Gzsd/hcyH/tSQEO+35izefAHrpT8cfK28CaVVqLajoW++gX31OaIH3jOwne+7uG4v\nPcqy5IGvbWh87UYOUW45VZyB9IeY5XVTp2QYoNtPQN2sDo8laqGEQKbcxKZbpCV98uwvzoHIEHpr\nFBo3R24z/pGf/jAU0kKM8EprYSEYMxmwXCLLoZVdI1PfGL2ddAiEA1oTSwdLpdRyVhFqj/Xcv/bc\nvH2Vajtye7BiVuK5ieO4G3tw0HrUQ4QtMpuvJOu3lodoJN8PQW+8yvZQtodd3yb2lxEq6Lq7tdbE\nto8VNXBqdxKBXnt04McwS/d79srnu0sVcaOBffE+pOjLYx+3xBOkV5ADUJkcVqPn0o7XRrvpO3QE\nGNq/Cym6ZUjz+Sy2baGUIggipBRIKSdaglq0NKpKpUKz2Wg3M8ni+6M7zs0D49Y+JRw0QCutScWo\nH4X/8ANsxhbxW29gX3xo7xlH/5jqFaw3n09/L1voiXPQgOuvINbvQ+eW2+lRmaFa3dMFu2lUGHRz\nbLWKUaSvDYvmcJtD0Shpjh8AACAASURBVLcWZzV2iPLLyUCiFtorDlqiKkZnikNr2xqoWXkibZG3\nHIjHNwVp4hAJj6y9g5VSmlPTtkZG3IxRFvDeyl57jzqOWCYTl4pbwm2VkSMs8DBT7I4r8Er4jWEh\nT7OehY57ec9BDRWHSMvpCkG97U1POov5OI5DsZjUo066PfUst/2sVdnYwdu+kkSLWy52I70Dl1Qh\nMggJSuexWpWBSHWh43bhFR8rbODUN9E7HsFAs5TZ5DmL+i72TjJRU7HCXlnBFmrPNiOWUxDIyuiW\npDq3NFD97iDivJdxPa9936NUKiClSO15vcg8//xzfP7zf0S1WqFWqyGEZG1tjSeeeCfvec97yU67\nzDchYgHqSMyaUynOhw0IGyV8++E9+g5an/29IXEet7v9pd9Cbl9HOR4i3LP+uDP40NbNBu7lp7E+\n+J9h2xb1ejMlQnyalpEQlze6ewkVERfWkZUUl6uKUfkVrHJv7U4GdXRxLakIpmKQTte1LaVgKLMo\npda2dnNEIvk6hk4eJx7TjlHaRFggoOyssxxdG9pE2+7oWYoG9AhxHpEGpWDfCUPcHj9CUsueoVBJ\n7+PctHsPrEgn+1lp4xlhPcdWhoq/AmGAn3Iv41i1rbZkCSYJEkx6KSdCkG83mRisR909R+UWXvnt\n7kRFxtHYb1ToL2OFtaRDWNRC9t0noVUyZjuDFTVxy9dRdoaokKSTzcpyzrZbmgJox8XekyuvhIVI\n+T4DqPwycntM+tee9cx4fXJxTqPT87pYzLGxsd3tyrW353Uv2Cyaac/rUVy9eoXf+Z3fwvM8vvzl\nL/J93/eXeeKJ4YIrTz/9+zz99O8ThgErK6ssLS0TBAFbW5v8/M//HOfP38P3f/9fZX39nVy6dElc\nvnx5fjMNYzmfDkaJsxCi21+20WhOXAt76SPfxOZP/32yf7qO8HtRx6POJ688h3UrWSNj9TzcvDK4\nQaMK6xdgK7EIxOZ1hA369lXK+fQ2gtOmiYW7gw8u5eVhxMMs9QR967syaKDaPxbRqiUPxr59dNhC\nCQvZJ4Qtr5czWhc+JUaLs7J7LrOG9Mk7eZxwsLWjkmPWEC0bMeIhN3K9WbpjrWqNoF/CmrZPxivi\n7Fk/j22PaM9aeOAt4TfTrWfl5pBt61kLSZAp0XAKKK1AxYRRgGO7Q/v2T9C0ZkiAO92ekliKTLeX\ncv3qVxHl6929leWl9rruXo+bRcTtKPw4aBd9EQNeA6FVMqmTDlKFeFtvoG2P2F9iFpazaOxit7un\naSEQfqG7RNMdp+2P/Py0M76edn9Pb53Jo/Mptd+npP+nNKrndSfYzPcz/PiP/11eeeUVHnvsCZ54\n4kne+c4nOXNmuOb8tMRxzM/+7M/wD/7BzyCl5Fu/9c9gpQhfEATEccR3fuef46GHHkk91jPPfI5P\nfeopvvu7v/PC5cuXR7emmwUL5uafBXepOA9/lolV4bbbJo5efxrXxtFZXcEqFAg++xTeN/+Z8YOo\n7WA/+1T3TzEiRUdIq/dIUTGx7SepVu/7T8YffwJ0FBBX97iZ42BIQLtjapTRey396nbyYBQg6jvo\n4nr7oRwlxUf6K3FphfaLSQBam7rd6/YTYqEdf2Szh1AOBpXtOGushbWBh68aEfAFo/0Kuq9u9xBW\nzxuQum+KpV7JrLLcKg+cL3IGuxoBySq2tFMjwUXbelZOloq7hJYStKIjamHQwracEZ6g0aK3t9uT\nEAKrdhtn9/rAeJ1xBVVIGofIqC9iX4Xd/PN+gZYqRNkZtIoRKNztN2nYGYQoHNpy9q89280gUIVl\nZGv496uUZuQ3Ykw7Ue1kELXebyNeu3CYoQ6RBMSN+5xiGo2YRiP5nL7v+/4yr7xymeeee57f/M1P\n8NM//ZOcPXueX/qlX57JeF566UW01vzLf/lrtFpNisUS3/7tf3ZoOyklH/rQNwPwyiuXOXv2HMVi\nqTtmrTVf93V/nHe+80n+yT/5R2PcYLNBHKDmwUnj9F3RAei3ZHtNKnS3EcT4fce74px3vofWJ38D\n90PfOvoLo2Kcz/06oq9EpCjfQeVKAw8CAL15I4mAbm+ry9tIz0JuXEOlrH1NlcNd32Hvg1xoRVw6\ni9wZbq0n0IjiGmz2JsMiaqEKa4hWNSlCImzQQXf7odvVJ57KzdKUg9ZLy86TGSHOSTBV7+9QuFT9\nswPBYeOe92LEhze2+AjjG2woOWy9xtImzCzjNnvPpmBUF6zcKlZKnW6hY5q5szT3eAI6E0SNJgib\neK6/5/3J3MW6toWzfQ1B4sKPvRLK8bFUC+GXkFJioWD7erdZSOzlB4S5g1RRkhKn4oHJnYyaxG4O\ntCZ0s9iV6+iVZQ5jOVu1Lezd5L5pyyYqrOCVXx3esDk6vU1WR3sGVGG5u5YNEK8etHzqwZg0Utv3\nfd797q/hPe95H1LaaK1pNA6eNrkft27d4Pnnn+PHfuzvkc/n+fEf/xEcx+GjHx00Bmw7iWOwbZt/\n+2//Faura3zkI9/Gysoq2WzPa+j7PpcvX57dAEdxClOpTt8q+oFI1mV93yOf92m1wgMJc/++oyh+\n20cJqiHhFwZbSQ5MCF74DHJ7MMpYQBKdvZcoRJXWe9vt3iG2MzhvfPEAYz0g9fSJ7bjymKqv5Z5y\nfKL8OnGm2K1uJVt9gUytKnrPPdNhA9VeL637wy76mnZJ7Q8NNNSwy7oiizQyyf3Twhr/uE+Ljmaf\nYLB9LMjOevleqt5S99o1gmCEu70RqVRrP3BL1ITP3u+c1qpbnSqKQuIRnpeDoJsVnPJ1NJpWdo1W\n7iyR5SQWehSgwyZxq07Qaib9pgvJ5yW90RG5Mg5QXh7V714XktjOEPjLyQRPRTSvv4KatFBOH+7m\n691c+2j1QmqIvoKRAV8qU0CM6829JzshXr1n2qGmMk0aVX9vgKQn++yCrrLZHPff/wD5fOLhefe7\n38OXvvSF1G077u53vevd/P/svXnQZeld3/d5lrPc9V16756eRTOjd8TAgBASGguQBGJzOTGJK9im\nnAABbGPsisupIpRTToUiqeIPvJEEExyXcZyyExbhBBtJiEUIZMrCJaFlJLU00mzd091vv/vdzvIs\n+ePce9977j3n3u6ebk1Pz3yr3prpe7bnnnvO83t+2/c7Go34nd/5EJ/97KfZ29sly+qjTHcDrzZ1\n5xv0nbeApUVYWo+17AVHR8MFhaZV513mmMogIHzTY2Qf+H/wc9WhAo/6/McKcpGqY0e9avOQlQvF\nHArZ30Xu1wjG3wqcLbFRzcLnSa2BFkkPH7cx7RMcnnuC3okHGTQ32T//9WRr55Hjqm4Y5xznziMA\nH3fxMuBQLdJ6eiEr6T69jiopNAH25SZ52B0TmdShPnQtaoz2KvIRD+Q1CzYrNVmjyFHasFW74PDe\nk8XlXKbRTXpyHAavMP5+JhyapqM5cZGb8yR8NkQMdlE2I22dKWybL8KSVV4x1mC9Y7h+EZMtJ4GR\nZoRrFLUENmyTNjfwAqRNpnUDLh3C/uXbqgrTR9fQB9enwizEMbKCgtPpZtGDXwEXL6YZZiFmW6x0\niKvQFH8luNd6nJ988ms5PDzEjmmDr127xsWL1VKlE2fj27/9ffzET/w3/NAP/SjPPPMZfuqn/lve\n//5fYWenvp3wjkOqV//vTn+lO37GexhSClqtmEajmLyrRSqW42bCxuG3fjem18P9638IO1cgHWIP\nd1B/8m/RX/wPteFTMeqhTi6uzMXBdfzsJLK/jfMedfVLtzT2SgwPaj1GAdhO/WTkNs7R23xoxuB4\nhA446J5ncPrNMCMkUNW6VCg7nao1WH1Z4REsU6ISgp3gNMxzgM+ipuXCez+dwD3lQKtX4XJTJ4Pa\n7wAwiNbwCPJgOTVp7sGNjbBH0Ndr05Wgdb6UCij28cjxpOC9I0lHM8QWk29SD29SGO6iXE7SOlWK\nDgil6/PvgFMBaWMTq5YthEDmA9zmRYwu30NhRrhJiD/tIQfbtxiH9wRHLyOSYaHDvXmuuN5gMUS9\nrP5g6SWkRPaPPW555uId51C+14xzt7vGj//43+Lnf/7v88//+T/l4GCfv/gXf6By38m4f+d3fpvf\n/d0P8/73/yo3bmxjreXy5cv84i/+L/zGb/waW1tbyyvu7gRebV7tN7i1bx8FtWVImuYMBglra63b\nDCmtLgyMn/pGsnaH9PIV2h/9VQLlyDleCYmjG0WhSV5RuFIRKhSAa61PWcPEqIc7cQa1+xJmeIBv\nltVxJhzgN/PdbJ4sfwiC6q1eKo7aZwvPa3asLgcUg6hLFjRp919GOItIB/iwWeamtoaDqD5MmDhF\nO2yWekwTv9wYeCTX7Ala4YjYHCxwYct5ghiKSuxEtfBARkjmAzwQi4zIpwQYtDuqNdBuhYGyQpM1\nNsnU6jkqHVdum7CNnTMqzhdqWbNfwTmLFArnLc5Z0mw0zT8v+/m9M9DfwaIROl5oIasqBJxeE1EU\ndnlHFm8QJgcoW+1Fm6hT0JHGbUR6zMUtAGFTZBjjsgSVFExjtnPupipv9eFlcAaZJ2SbDyAkOA9B\nOljY1y/x8MWoXpzDdTbRvRk2vLMP1e57u7h943z3cqzvfvd7efe737tyv4mj8qu/+n8TBJozZ87y\nnvd8Bz/5k//9dJ+f+Zm/B7ABLOFGvQN4DbRSbW1tbQF/GRgB7wb+x0uXLn28bv/73jjPi1RMKiNX\nFXbV4+b6iMMn30r68T/E3riOfOSxEuOWcBa3cQaxs9ifKw5v4JReEGUQw7lCsdwgfIbcfg778Fsr\nxngT38RZUrf8IXDpCBt3UHMKQ+nmg2TOE+h4zPs8hsmQQRPnPbnUHKw/xtrR80iTosIIOy7M8Qh2\nGxexugE1EztAGnSIZozzoCLfPI/EKoami6LJSbVP4FMkDu8sSoIPG1gZMfIRRyYmR9OQpvBOYfrz\nJsQkIkZKQSjarJkbyIrQt10hsAHQizaWS0mOYSjITPpVoX7vUTLA+/IYnLdIIXHeYa0hy1K8b9RG\neLy1uP4OTmiE1KXCxOI6RfFWHXzQPPaqvSWL1wjSI/TcMVY3MEIXi8s8Q6gIOftbe483OSpqYNMR\nMusj+y/juuexy+Qb0yHBcBeRjorUSauIpoia3LXo7RdypKcfQnYL7neEB6nQ6QjnLuLSDPpHiIPt\n486JqAEzj/29YpyFEPcEQ9ik5uGbv/lpvu/7/gLnzhULbeeKeoj9/X0ODw9hQpN2N7EkcnUvYGtr\nSwH/APhPLl265La2tv5PWEI3yH1snCdaxkGgSyIVx5iEp+98WBsgeNd3k/7JH5HuHqAeUQttHKJm\n8hMmgxPnYfvF8uf9A9zaaeSE13r3ZdyJk6j9q9hzjxeqRdMx3tzCw6RDvDOYqINO6z0I09osGWcX\nNDga50e9Cha+ixaQTeWpJNdbj3Ii3yYaT8weQb95nh4tlIVgSTSiZwOiMWOYVyG2viGmuJwoPEwA\ni+a6nSmmwyIzh5eKeeGoQCtsVv2uWA8DGgzUA5xSe0R5eaFkbmJicDLEe4H2S2QJxxjGJ6bfYR7G\neZRUCwVqzjsEAodkYDTJ3pDNzqKn7pzDDPYQ3pMEXTpmMQwslELY+ofHSQWzhtA78mgN6Wxp8WKC\n497iomLf46Qu8aF7ZzFpgpgs8tIBQbJH58R50GGJKAUAmxPtPlsUlKUZ+YkHps+OqMg3Wx3jT3SR\n7RahLCcsTBCjsyFKeWhqaG7iTm9ijMQPBoXYB+P6CCEQpy/CkjbL28G9Fta+Hfzoj/51giDAOYcQ\nYmq0NzY2+Lmf+3lOnerc9Vaq14Dn/HaKR+lvbW1tNYFd4J8uO+C+Nc6tVgPnHIeHi2EumBiu25WN\nXL2fOv8w+sxZsu3rNLZfwnc7pRye6O1BewP6i89trfGPYhgXQQuT4cIW6nAbufMC7sKTs6PkZsgd\nzDgEaML2UuM8f57R+gPTlaqxlmBOqQqTgghACLxJsaLF9fA8IQYdew5toyiyopjjI62LMGsVhCAL\nO4SjvRL5SC2WGEolRG3+Mavhn5ZCkE+8OCG5wUlOhZIoK343j8B6ufJRMl5zlDc4pVcb555tE8q8\nVnrSOoESktnSZO/BywDjNc6DM47r+0MCJYi0wHkwxhDaPtrljMJ1lLOVRXBVvOcTOCHxVYxh3pI2\nTxD1ryPxRfFbRXuel7qonp6lf8XjTYLXMU5o8tGQ5PKziCAmXjtJd20dKRVZMiL70meAomBNpX1s\n91j/Ww7Lz7BTIeb8Y4SDnYWxFBdefFYkEGoHa42iGHKzg/OyoFINYu60E1gY5zt6yq86gmCs6f5q\nUmjeA5GEFXgIeBr4y5cuXTrc2tr6v4AM+OW6A+7tWMArQK83mjbuV6HwgG/9vLfSRxy85a145zAH\nh7j2otyjayyGLgHE0Ta+Qr9ZHN4otST54RDhHeroBsy0Lt3MAsJZgxuTiFg8ftkBNse0ivF7qRiG\ns+P2MF/o5OwMq5An1oURydDkujk1zNPdV6wR+zQLIy2XaxgDtR4ngJLVs6AUjjoeCK0Xz3fDb0yL\nzrxaQhM6g5ENyb3GihXfQUgSFzJyjaWTtkNOC+48ipwmidUYB0qCVsW23Hr6qWOU5UiXEdgRSbiO\n9xBR3e4il6QZfNCsbzlzhrR9Bg+YGrlO4QxeqAUGNy+Lz7wQU7Y5nyeMdi6z++VnuPGlT9H/yqdh\n3G+uhESeujB9F70HOdN14MMG+YXHlwvOmPp2Hxs2kDZHCtDSIdZP3BUPt4hw3fp574Ww9j0FpV/9\nv+U4Ar5w6dKlSdjtj4D3LDvgvjXOq3BbZB23CPXO9yGjiOxwAEcVEoyD/UqjKLyHjcUqaZGO8LOf\n710tKBF7+6jdF+b3Xjo2M1M4453Dt5ZrRduxMco7ZwqWqtltFdfSM2FXNZMjddYw78WkK+iCHQIb\ndhitKAYDMK7+ka77uYMaow1gq3rfheCKPYEIm4jw5gpRh7YwRvumekE2gRHF+XIncUsMuffghcb6\nkMRFzEahrQNjPVoJpIBQOrSE2I9Iwo1iIeI9qqJVygu5VBbTr6p8doakc55lURvhLV6Iqd62DVpY\nUTCwifFf0Z4SFMxsKkAIheS43c2kObM+v5LqeNHQ6JCffxShBDKr7mH2gEr7ldugSN2U/t2+W8b5\ntR/WvifwardRrW6l+g/AiXHuGQpP+otLv9IduC2vSdwuB/WtGHW1eZrggYvkvQHu4AZuTstYpEP8\nenWrUh11ZWkf7wr6xME+or879Z5vJipgk/LEZILlIWPvchyCYXORKMU5i58TYPB5OjXZ3uZoUUxA\n1nmiuefYA0G4/Po91SW/iSxMausf6TquCymWhHFrNnkEVzlNKlYvGIoe5WJcmQuWGt2+OTb2Qxsu\n9Z4NASMXFeIiFft55wikw3qP9jmZak6NuBauskBtvpp98Zyri9oyFZGG3aX7CO+KPHn3NM6ZBW9c\n2Lzg7DY50mbIbIi2MyHlMCg943YsyeXCBvnZh8fl4BJVY5zdbFFb1fjm92+fvCtGtPjt7i/jnOc5\nX/rSJZLk7teBTVEQV7y6f0tw6dKlPeC/A/7R1tbW/wCcAv7hsmPu25zzKtyu53yzRr1g7okQT76V\n9MvPYgYj5LpdfOtrwiGyv4/tnih0nWfPu38dr8NpSM73DiBSiCxH7r6AO//k+PrV4woCjTfDsQd7\njCzLCeakIEvXdZb8xENkutqweB3PET14AinIxtYtUhZjiu+qpSO1ZQud5Eu4jwEjIoSU+BqiEJgY\nlmrjLIWnvsapeoOn3qADGBT7eYe2Wq4/7ee5wE2bTVUROpaa3B4/D84LctEkZNHAeKFJxvcwsxIp\nQMnjwYZaYk2OcZO+Z4mZ+ZqhrwlpL/GaCRsLrWmL45LkXoJQSN0kMPXsWzZsYZIR6EIvXeQJEl9k\n0oVEIFE2KYyoDhDjugCrIlRWXlzKpGChy08/PDX086x0pf2DFf3ZM0WONmggouZd85zvdVnIW8WN\nG9v8jb/xY3zbt72Hv/N3fpJTp5ZHi+4E/L1fEMalS5d+A/iNm93/vvWcV79Ht2ucb4KEJAzodptY\n63Df8G70+hrZ0QB/uIefC5OKw+1CNKEK7UUyDX/6Iv5rvxn/5NtxW98Iwx5Wx8jDG8j+DnbUK9H7\nTa8jCgKWOA7o7VapTXlMc3loO43r1XjsuLK1BJNOfwjhMiZG0Bi74K1mlqXc1sM8YnvQXBGsrz8+\nDiXVoX5HHWtrkbZdMsEL2E3buBXec2LLC7DEhVDR85yzeJ6RUdi5z72HxJYjFc4XRjqzEuME1ua4\nKSGJKhlmAOUWjbPzFHrbNd9ZrFBvgkLFarIyTFQDW5N7trp57IX7os3NqRCj46JvXAYoU9RUJI1N\ndHachsnDTmmE3nvU4ID81EOIYGaSXkbHu0T+06kQOcNBYJsbt9l2uRq3F9a+t/LNEzYxKH6L8+cv\n8OEPf5Q//+f/cz72sT9ccuQdhJCv/t8dxn1rnFfh9l+0+j5nKSXtdoMoCuj1RiRJhuisox9+tDDO\n3mHTvPQyCmfx69Xyj3JwMP3RvZT4N78VffIEUhQpDhUpxNbX4aJOkVvzEnl0DWtMyXOeXSzs39hZ\n8JonMEuKGjywJ9bxNY+M9w7CxcIwPV7RemdpBMeDaoYV51ki87ifhOROLS2oMsuKwVT1bxbI+uzo\nqrXbRArj2nAJIxnQyxbv66Fd9CYSV2X8BH0TlYrmvIyWildG0ky9MUO0WMDlXUka08mAYbDJfvgA\n29FFrjceYTt+mIP4PHZGqONmGLDN3G840p2FPnCHwFbeW1+MDYHOCwGVLOzinZsqXJmwtRDd8V5g\nG118q1xEKef10af7e1hCPiJb5ZC8bW3etdzwaz3n/NJLL/IHf/D7038LIbh8+SU+/OEP8tRT38B3\nfdf3flXG4aV61f/uNF7HxvnOhrXjOKTTaZDnZkx2cjyV6W96L0IIzDCBNMGN5nIxNat4kQ6Rp8YS\ndW/6OtQ4WSvT/rRgRUgQ611cECOSITo5ZLB3HRBIKaaLhX5/xHA4Il3ClmSNKU3Gpe8dtsjRWFVP\nQTnPaAWU+l5Dcfz/vuI7J6Y6dyqlnlZhXx80avOi86Hy0vhrQoezoeCFY1Z4KJMx5T5g5Go4moXE\nVQTsB7kuKVlJpRY87JmTMLCNYmHkl+fVY+WmHrOTTQa5QvqyMYuEHffuKg6D01yT5znwnRIDoROS\nRMTcCM7Tj89gVbiSS9sLhZkjD/F4RsE6dia078bKVNUn8QQ2RXiP0TGpiojNhLgGetEJgnyuPdJ5\n7Mlzpfd50mpVBRcUldh1MHPPSueBR2i1mmPt6wil7ty0+Vo1zpMxX778Eu9//69w7do1rLVcuXKZ\nX/7l/4OPfOR3gaJ976uCV9trvgue8xs551d4nFKKVivCWsfR0bDyRVNbbyW8eJHscI+g1cBnGU5J\nZFRMWOJoB9/oVFIJijDEX3gM1ZjzKmVAwQIHwmaYC28meOnz+EaEHR6SSsnamQukaU6a5njv6PcO\ncc6iqQ+MmcYaqrdYyDEKCu8w80HtQ+OswesIMaPdjMlQYQvrHCZL0DLAODDWoQWlcKvzIHWInwu5\nJu7YiHkvSVxMKMoFc7PkIxUjI81rQrVLfFCzwlVMzbHR3U7aPNQaLZKDLHnFDvIOm6qoKZA6pqaz\nqTiPFwxdm0hmS6I+vri+B6ta9FNBU2cLgp2By3AyZEeewvjZ8VV/4b5oMQxbnFA9XLKkwlkfh7TL\no/IMgzYNIwvRiyWFWFJIhM2wMiQJu+AcQVrk9PNoDSMUMi/nsW2zWy4WA5D13ODzxYvzmG2xcipg\np2/oqqxgigtD2u0mQogSQUqe57cVjbtdhrBXG5MxPP74m/nO7/wePvCB3+Tw8JAXX3yBXu+QP/fn\nvq+0313HayDnfKt4HRvnmyvsqjtOCGg0ljGQlRF/49P0fvPXpsbdjRKQEhkEhcBEewNVYZy9yRFn\nzi1yRCe9grVoMvFKsOtnEF7R9Dm93gFZkiCaGzjvyLMUOw5ni6ABNdXgBsl84NgDR6IIw+Z2nJOr\nyFlCsU2ZsocVKRiO58mGtvSy4kWKtMPkZYOaO7nwUB6MyiPaGTa42MnKMolLVq5acEzNOT/emnlR\nCpZSSAqKfPDMEexma5wIytKEma83BIkLcTpC+pTsZtrELKS+TTt0mGy0sMKKpMMSMLAhzhQbY5kv\nxO2t0OyIk5RP4JcWJjmpuZJvclpZlK17dpZPJyPdJNANZM3xeI92KWm8Ptbs9oQuQzqDR9ALN4hc\nWhq1CdvVPOBL7J1YUtTmpSq1X9nmBgiB944s8wyHxdillASBJgwD2u0mWmustWTZsbG2NyGF+Vr2\nnIUQjEYjwjDkxo1tPvrR3+f7v/8H+IEf+K+meWj1VTKadyOs/Grjvg1rr3reb7/Pucg5d7tFfuvo\naLDSMAOIb/pOgo01bDKzKh8MpwViokK20QuBP/cgVPQgC5vjVYQf9PEHe8i9l8k3zqBNihjsg/e4\nPMGMDhkN+xgz02u8pFfVO4uJyiHaIqR9bGSMqG97stYsvChmNJguhHw+mi4orLULnmvuQMzkKLUO\nSCvCvdcG7XIrjav/TnXkI1q62udk1aMRBmoh/97PY7woG+PELPfS9k1xr48q8tLzkBLSHHYHkqFt\nIlWI1hE6aCBVREqDXh7hxosKgYe5kLYjYMdvLHxBvaSdDIqFiheC65zC6MXUhkdQwRu2gJGIGegN\nzFhoZBZCaobRRmGYx4jGvdhZYwMrNeHMotIj6DdOVvKdywpRGSjee7mkv9lGndIzaaatg4JZi++c\nI00zer0Be3uHbG/vcnTUx1pHHIdsbq5x6tQm6+sdms0GQY2AzGvVOE+M7+/8zof42Z/9GR5++BHe\n//7f4vHHt/jxH/8Rfu/3PgxQSu/dTXghX/W/O43Xued8a8a5aI8qhBB6vVGpSnEVZBTTfOqtjP70\nT9CNY0/Q5zkiGNsZFAAAIABJREFUipCjHq57Enl0rIHqHthCSPATzyDPYNCHYQ836COSsgei1WfJ\nG23EmQuEj5wiQxTtTXPVxJWUm7Pbww56ZgKbhLQnSK1cyoctotaCRrQSEuMd3nsa2jE0avz/nqEp\nn8iikWNO+L6pXgjkTrGfdFiPetMx1aKurUy42vaqVflmUbPA2U27nAyP298St/wVS11IplvkZvWz\naGfC9rkT7I+OjVgr8Iu50siVItVeBAxMjBSLz62Wnrpos/cz6Qch2PYnOa130DNtUjfFlCbUNFIx\nIkTqkEArcmPxflyTMOcF63yAk5qj8TMYmON8c9o8gaps8K4nGHFBAz1aJASaHjq/sGwVxvlmjGjh\nMRvGLddIKQlDTRAENBotlNIYY6aedZaZ26wCf/XD2loXz/XZs+f42Z/9+zz99LdgreXpp9/F9vb1\nr3ro/X70nF+3xnlp3KsCs5KTWqtbMsxQrNijd/1ZRs98qvx5nsM491xwUhdvq2t0injs3jZyNMSP\nBmVifx0yyTlPIKyF/iFISdQ7JN96Jz4CFUTYuRlABI2SFOMsrC96TSemoCfKlcXOFwL2ylYfn1uL\nRiAE9PQpeiZCWEE7sDR8D+9SoAGI8WRcNqypgaaSCAE3jurDvUMTEKgm7WCI9fUvZ210sewMlY9Z\n8XjkNYuBgYnYjEKkz5glH1mGQ9NZSiEKgPdFX/P+DvJjH4LeAWI0hGSIXTuJvXge//jXwfmLiHFl\nV6jMtJtIhzHPHXQ4006oCvRIfA2T95gz2c1MtmMDfVZdn1J9ztNxVsEJXbrfzkOa2+n15w2zcgZp\nM/qtcwUzmXdTUhEnNUfhJt180dDKIKwNXa/KN0tbzjfbuHj2b8fDdc6RJBnJOFomRGHUwjAgjiO6\n3TZCCLrd9kzu+qtUQPUK0O/36fd7nD17ju/93j9HnheRi0kI+3u+58+ixp0fXzW+7XsgD3+n8bo1\nzjcb1pZS0mpNJCdHOFeErW79eqDPPkj40JuwNy6jouIc3li8cwgpkelwKtotsyH+2gvFBFwBsVDm\nM3Mt5xC712h9/LdItt4OF55YoNi0XtaSfnjvsPE6MjnABU0yFie0nAhVQY4xub6P2hzYFiMbFjbY\nQ+5DdpMTnIsPiZUnsWLMGOZJ53prvAwxTrHKSzhMY5Tw4/uxuK8SbhrmXfyexR2U482zipFLJQuB\nflq/fSftcjrcmSu2qscg03Sbolic1UDsXEP8v7+G+sMPIMycZOSjX0v6//2r4h/tLvKptyG+6c/g\n3vlkIacoFM8ftIEid1qFZUValbzrQrDtT3FGXkM4Q75CLWwVoUsg3UI9WmhTTNhiqIsUUuSyach5\n2DqLl6rkvU+glrzX81Kss3BSI2f6qU1zczrp34k+Z+9ZMMBnzpwgTbNxJXiMUgpjTCl3/dUkKUnT\nhL/6V3+It7/9nfzNv/m3K/eJ45gPfODforXm6ae/hZMnT063TcLYN25s88UvfoE3v/kJTp3auuvj\nfsNzfo1hWdHXzRSExXFIFAWMRhlZVt96cZOjAQTqa96K+aPt8pbcIKIKg7+MxzjPCnaxqslm0MNr\njTQZjWc+xkhpOP1Y6QtbZwvpwRoPw4QNguSANKju4U0NxEpDDaNUz3cYWV2yrUluiQPN1WSdjSiF\nMTuyFpZ07lHMLOyPVgtdABymEaNccaY9GrcRHV9Uq6KIbYKC/KQg69jJQ1JznDsWOFqBoaENSpra\nxY8UkJp6j2BkQmwUkdrV3iR4DpOA3ZHkkfVkcVHgHHzo18j+1T9D1eTvlM2Ovd7+Ee7f/z78+9/n\n2v8qCd/+DpKNB+HCI+jzD5A/fh7RKffxBoVTWou6KngnFLviNJvcwK16maReeo15rxkgMCOOouOJ\nPxwXktmgyUC3Ed5V605n1QVnfkm4G8DGHYLk2BOfhLTh7uSGJ9SdSZKSJOn0OkGgCQJNsxkTBG2c\n8+R5zkc/+lE6nS4PPfQoYXh3pu5f+qV/wuOPLzemWmve/vZv5rd/+wP8i3/xz2i327RaLZrNJkpp\nDg72+dSnPskP//CPTTWe7zrucT3n28F9bZyXYZnnrLWi2Yyx1la2R02OvZWXdbIYsG96G/oLfwIH\nx1W9RWi7wjhnSS3liRACHzdgUNF+5R2+tQa9PQTQ+OwfYd6xQdI5WdrP6xiRVUtqWutwQnIk66n3\nfNBBpBVSrSpiP4lphY58zl0KlCPJJftpRDsM0H5YtFVJj3GTQiY4GLWQUq2MLws8vVRjveLFww5r\nUUY3ygojLHyhViQEXkYcDgX9TAGStTgjMeXFj0fSz0Nyp8ksnG0Ppj3D5WuujrjsJJ3aQrRZKFHk\nzwH2k4hulDL9xZ0l+o3/HfG5T5IvK6y5fqX6c+dI/+TjID6BGvcoj975Lpp/96fLY/C2PgrjWVro\nlRFwqE5VUoyWzrPEs1bCL64OvCfXjRKpSTBuoeo1z4AQRDZdGJn3wKAwsE6FmMZaUawjJE5qVNZH\npQNU0l9so5ub4O+2ca6i7vTek2U5WZYzGBSLDKUUYaj55Cc/yR/8wUe4evUab3nL1/Dkk1/Hu9/9\nXp544mvuyHg++MF/x1NPfT3PPvslRqPl3P5JkvDe934HL7zwPP/xP36cZ575DHme0+l0edvbvomf\n/dl/QLNZz4lwp7GsyPW1itetca5CuT0qIc9r8lb+1sNc08VAEMHJc5AmMA5Ze2MqFwvCO3zchKQm\ntC3qu3S9d9OJSzhL+xMfInvHf1qSqbR+2QPgyVunSSsoJSfoZ4K2F4i5St+J8tIwl0SqnEtNc0cz\nKLalVtK3HTaiYck4Zy7mIAkReLoNS7aM7lk5jmbakA7TkMN08u9CrrJKqaq+VdgzMgrnBS8drXGi\nMaKh09L+Zkl++3gfvdwdneL4N98fxazHWXG/rCX69f+N4E//EO89fv0E4mC3+gyjAZy9ANcWjbRw\nDn/xIXi+EMCxn/vswrMmxouYKkglq5zaEkY+xnhFU9azbi1bY2nhFn4QhaevZxaG3qPzIXnUJR1T\nn4bzvc1QRJPCmCRex6iyOIZXEUiPjVv47imk88g8QY8OUdkQOZNWcDrExcfXv1vG+WbOaa1lNLL8\n0A/9CD/4g/81g8GIz33uczzzzGf40z/9xB0xzs899xVeeOF5/tpf+wmeffZLK/f/4Af/LT/4gz/C\nyZOneN/7vnth+1e7Av1+DGvff7GAW8Tk5Q0CTbfbwns4PBzUGmZ4JW1Y4+Pf/M2ojTJPtVM1RnDZ\nQ2cyqCm4EP2DUg5WZiPWP/khRHY8oTnnoO66wEjVsF5Nj/e4YK7tSjUYjduHvKfwfufgcQg8uS10\nh1/sbbA7apK5mGu9Ltd6jfF+Ynlon+Oq0So0AltpmJVwtWHpWJdz1LujBoO8zJo2ylZPBAJ4+SBm\nVeHhfJX5y0ctpMuJfuUfE/xpwUsshECeXR4elJuLamFTNI9pLf3RIe7K5fL2pRPp6uc8dZq9rEUu\nqj0lj1x+iQrrn8lmKQ2jvQFn6MWnjj+b65f2QBavM2idxOpgIW0lZlquhBB4JbFxk3TjHIMzj5N1\nTpJ2z5G3TpB1z5WPvQvc2rdr8DudNZ5++l386I/+df7SX/ord2QsH/3o7xOGIf/yX/4yn/70p/j8\n55/hV37lX9Xu3+/32d3d5Rd+4ef5/Oef4eDggL29XbIs4/3v/1X6/fr0wd3Aq91G9UYr1R1GYWQl\nrVYhu9fvj26KOKDA7Rtnd+ohCGPExgn8fuENeWOql0pLBOEFFJ71cPFFENbi1k4g+gfTz/TggNYL\nn6b/+Dumn3kVlniWZ7GdrhHrnGWsyokLaM7k7w9Nmd94mAkaQbkYyDpoR45eqnDOoYSjl4VFGHyu\nX/lwKFiPFwvGJjgY1v8OkfJUrbGaoa1vvao43X4SEyhLIHOkgGxFexQUOeleGnCBZCkndS8pnyu1\nCvvvfo3mZ/649LmKA5bW8S7z0uciL/Zzn0U9cBEo0gJVofsJ6orpJpACsvFC5/qoy0NdgZ1PlUhd\n+wgpyYJAxcB1iVXZK45sQh5vkk8Wk96X5CA9gn77HKFLq1nKhETVPOcAXkd4HFYpLDGmU14MvZqe\n8/wxd6NN6Qd/8Eem/59lKaPRiO///h+o3f9Nb3qU3/zN3+DZZ7/Ihz70WzSbLZRSNJstPvzhD/K+\n933XHR/jMrzhOb/GcDPPfafTxJgit3yzhvlm9JLrxjN5sdzJB5Enzxx7vv2jyvlLWIOP6tWAxLJW\nhYpBhrtXCHvHqlSmSk0KQIYMTLigiDQPYz1eT3i+A4YVpBuuIgycGk87LELeG43CoxlkgkawaE1T\nqyonsUC5hbzxLLyoNqJqCeFGWnO+7UELUDeVbwboj43u1cOIOu9ZCj+NMkzQfPHTtP94UVUuSg8W\nPpuF2LlWv+3qi6UIi/38Z6f/H6zIi89zZS+ce+4Ze+GoBXNKVHKJoEqky8fnNDnK48V+ZzPiKD4m\n4wlnKre9kPTb5zEyKFPHlgaxqjjPl/7PzRHx3CvG+W7jIx/5XT71qU/yzDOf4cMf/mDtft/3fX+B\nt73tHVy8+BDnz1+g3e4gpWQw6COEIIpurpjzTqHo13h1/+40Xpees1KSZjMGBMPhaGkIuwqvjF2s\ngHnsHUT/4deRZ87hrl4pvAcVVItg6KDIUVdhCYG/qPCoVW+P7pVn2Hnzt4IsjF4VneeQYnIamYCW\nSpYuRlIf02BEQnVYMzWCVigXisMyW+SfR7kk0pbUKOLAMcrLBnKUS052YJCUj1+2Vg6kZZAuLlyE\n8GQ1bGKBtAvGchZXei1ON5cXykDhjR6MimscJiHn15LKHmI5d09lOuDCb/1cJd93MNjFd9cRR9VG\nWvQOcCfOIHevL27LEsT5i7jLLwKF5zyBEn5pf/Uqz9ktpA0klwdrnGsconyRq8+WvF+z/NdOhNxI\nurT04rNudYydMbCRK/bxQnHUPo+RmqiGUra4Tn3cwUPJqPuguZBOer0Y5/e85zt4z3u+Y+V+zWaL\nb/u29/DUU9/A+vp6adu3fut7iJY4FHcDb3jO9wEajZB2u0GaZlhrbyuPdPu83DNGPWriGmuIk2dg\n/CA7UzOJ5UsMsPfQqDaKIktwjXKYWeBxuaFz/bjoo6rScScrimFSU6bTrEJmwcmIg6z+hRxkklAv\nPm7WOQLlaQU5SjhGuWQtXrwPuz1BpI9/LCk8+0n9uJoVHjhAJzS1ghahXvWjSq4eNha0qOehpS9R\ne17rVd8XMxdaP/u7/4TwaNG4wjicee6Bpdc1m+dqt4n145Y4d/UKbn/SLVAfLVqmrz1BUpm7l1wd\nbZDRKELatfDYcdpGBg2up0UdRkPNPe/eM1Dl53hSuT1oncaMr6FtjUQkot6jZty1MEvNGS2vtbhT\nKIzzV+VSdw3zhhlga+uJr/o4PPJV/7vTeN0YZ60V3W4LKSVHR0OyzNwWhWeBuganFUfNGXXz6Dch\nrEFdKPJ/DHrVrTs2xwf1YSKhl4Ts9OJxPhnR3v4yekyxaawtEU3IsFXis87catKVhHaJXrIKg0wS\njA20FIDQDE3A0CikFGzEGeDGdCJlo+ER9FJNoAxKGGJtaAU5J5tDzrT7nOv0ONkc0o0StDS1YaY6\n6haJH7dZ1SNSlsMkxNXkvydwrrx9fxhWhtIHM3zanS9+jI3PfnjpeWdpX6uw9FmeW+BNQtt1UprA\nyiIXwfL8+3ayxsC0ascVKgEIBr7L5f4afuylR8Ecm50Ky56Rd6h8SNrYnFZu4x2iqucZQAWryFhL\n/3JRffvgncTtes73girVvQYn1av+d6dx3xvnCR92sxkzHCYMBsnMC/FKcse3M5pyODw6/zAibCC7\n64iLj4AxY1rOCgRLDOSy0HYFIYM+2sUD65c/PU3Mi+CYw3onK5NU9FO5ouYYDtJ45aThfVEopZUg\ncwGDTOG8xHtBPy1aqzYaOZn1nCoNwaFkUZAVSksnygmVoRtnNAJDqBxSeAJlaYU5p1ojIp2hRDmU\n2QxMreZzpC3WLR+/GudtXzqIaIT1+w7zxdfq+tG89+w5SsceXz7g7O/94tJrA6i0vlUJQM/UEszD\nXb9a+rf93GfJraZnmiQ2xvhwoc93FUvafFi+Cvtpkxd7mwxNc/p8CARCSCwh17OTHGazkR+HyY+9\nXCnlQg47JsfpiH5w/JCEuFoDLCqEMSbwgJjxuJ2KFjoY7lb4uagAf427zvcInFCv+t+dxn2dcw4C\nRbsdk2WGo6NFsg3vb9cDvl0t6OK/k5y3c57RmccJrn4etXkCkya4LKteMS2RuRPO4RptxKiianvY\nx8dNxMyEJ5whlxHR8ID44GWSjQvH4UcVsjssh8k9Ai8ihK8ODQoBe6OQZuiJVX34EArZQ+vC6cQ0\nex9zJ8idINaGJLWsxcXVlZgsiIomrMQUitRCOCRu3GctSgumQDk2mwmDLGCYF5N7qB0mk2jpkcJj\nnCyauryvNdqz6CeTX0ay2w9ohjOEITM4GC5GMvaGIWe6xwxgWjINhT38lQ/gOhtwtL1w3Cwag+sM\nm13UcFHBDEDvXcV21qBXIezQO0KcOo2/UVxj8JkvQBozMuUpYDMeshkPcM6XtLar4Fas7QWT+yrY\nTVrsJuXQ9EYjX0gxtPSMIXWOsL9LO9vFe4e0ppCHlJo8bBFkffKwDUIQ1HjNXgWoGnlUKELasyxj\nvsJrvnvG+d7LOb9WUUkx+xrHfW2cnfNL26NeSe74dgjdvfdEUYDW6lgD+sxj8PLnEVKgzl3AXnmx\nUKqaJyTJErzStdzAttFGVxhnANdcQx2WJ36X56Cge+0Syfo5sjwnUpp9u5hDAhjlmpauMbxC45EM\nMmg2FW4Ja0UzUmz3iseuERQecT4TJlbCE2lPkoNxAosid8Xnk8ri41sjcUiMFeAdobKltm8hoBUW\nuWwhI46SgMwWodQCnkg5WoElWaZqRSEvORk3wG5fsXFaks5ZsED52gryq4cxp7sJIKYh3MbwBg+8\n9BFeXtuEGqKv4+8jMKcvop7/bO12zj5QbZwBTpyGsXHWL1zCpSNQZWO0lzTZS2LOt/tIubx7IV+x\noCkyGNUvmMBVksvEKgdn6Pav0kgPkL6Q9RQ2Pz6TzVH5iHiwg0dggxinA0zYXuj7X1EewHyVtm0s\nPv930zjfuqTi/WeE7gTuR4aw+zqsbYxb2h71SshEbvUwrRVaa6QUHB0Nj8nvhcCcfAgoaCbVuQfw\nzYqclxDTwrEqqLmCl9mVpDeLYT3V28V7j86GNHeLKl6iDjfS1sK+MC78qXkB+vksQ1dQy7shgMPk\n+ByjXNJPNc5rpNRoKdFKMjSa1Gksx8IXuqblx4wNu5CSxAbTf0+vKSAOLNblY0nF2e0C8OyOQgaZ\nJlamdhIO5KxOV4EXdoKF4jC1ZNF2MApR48tPSFAe/dK/QXpLK7o5NSLZWkGJGNanP2bzw8JZ7Jc+\nV3cV9pMmR8nyitvqYrCbQyOYowx1jseGn+Ds3p9y4uh5QjPEK42VutA1l7q61RCPykcESY/G4VXi\nw6tEvW2CtI8U1PbwA/i51isfdYqOiflr3AUCEjjm1n4DrxyvdhvVzbZSbW1tNba2tj69tbX1c6v2\nva8951V4JR7wraxgm82CEtRaQ5bZhRfSXngSvftCoUylFO78Q7jRAHH9ctlTrnmRXRjjOhv4k+eQ\nWiG1RkqJsw6XZpAMcSYtVK/GkFlCrk4TuozO9S8x2rjIdrrOsvVa5kJCUQ4RSiHYGx4bhMxKiDRU\ntK6EgaA3mL9vgtwW4hTtyNPPFq/f0DW92BR50YnhVrKgzTS5I56p1hYCmkGOFJ4k14xMwa8dyCLP\nPGkX2h+FNAODFH6huG2QLC5McqcWfpL+aPlke+2oyanOkF6q6R58mdPbnwCgywHbQYzMa4qaxoh9\nv1baEUD0D2vvlTws56TdFz4DT3xz5b7OC24Mmzgv2GiMFs6pxHFYvg51sppQ9Ffnkxy/czyWfpJQ\nZAUbGm6c0FYIXyi2ISUejREKD0iToWyOFQrp3bE2ubM4FSBsTtjfwaqQrH0SGTaQ3uFGPcRYrMWr\nADmTj7aNMmvfBHfXc37DON8JvIY85/8J+OTN7Pg6N863G9a+ueO0VrRaMXle5LzjOKo+Tmns+jn0\nuI1GOINbP4nvbiBuvIwY9AoVqjQpqla1hkYL297At9oorVGiCAHrGXYmpRVKN6DVIDtzHnf9ZfT1\nF6fbrQVE4XXLG9e41nyETmQqWbUA+qliMy68zQmkChYm6YNRwEZsFyqj59mwZiFFNQtYI/DjCWxx\nW2YEWs1V9o6NRqG6Vf68HeZo5emSM8w0B0mwcN5hrmloi5R+WmIUKcvVXnWl9JX9mIubx7nk/Yp8\n8yz2h5oLGwGjXPM1X/z16ecKT3b6YeIrX1h6fHtwlf2ogUyr86hi+zIujEs0rdNr3LiCa3WRgyJn\nrb/4aer8ytE4NL87auC84ERrOLcQWfECeE+2LOw9rhPAOx41nyEmWTijQ6BnLioAMUmZKIXRAV4o\nnPcIZ4paingNLyXSGrApymbER9cYNU9gVAAqRERtlBAo7/BurOwWxKhmF1PRzngv5ZzfqNSuxt2g\nz7zT2Nra+i+BjwFPASv79e5r47z6ub/dwq7lxwkhaDQitFYMBsn0hV92nLnwdajDa0U/q/dFAZjS\n+LMPHps4a8HmiImQ+cJ168cspEKfOUPe2cC/+CxBNiiMfrswOps3nkE/8FaECKiLS3sElgjF8cTf\nzxbDqNYLBiaiOUMmEWkqveIJWpFjULG9GUI/ubXfqDDQCsGkpcoTBSGDZPwbSE8zNEhZGMv5xcXI\nKNqhGZfyimIRUwPrJdYKkIWAwzBf/Upd3pOc3v4Ea4fPlT5X62sr884Sjz/3EDxfGHFz4hzh44+h\nA0kjLIrjUtEk29lneHkHefX5qf6zEAJ7+iLyuWeK6z376YL8Zi56pKUrtXntJzFKwVp0HHlZJf4R\nVGh0TyBwGCuQ3vCQf5aG7VeaerGkCBLAS42cSJZKSRZv4HWIoBCusC5GeI/wFp2PyIUqPHCTkeuo\neJ9UDFrSPHGO5noXKQVZVugo53mhq3wvGec3UA13jxvnra2trwHecunSpb+7tbX11M0cc18b51W4\n3WptqDeEhQ5rVFshXoswxm48gD4oZmdpctw87aFS4zRpTa+uM4VgfIXGss5GeK0JmiHm8beQPXuJ\ncLhP0nqIWKQELuPBg0/wvH6aSNX3CfcyzfrY4RQCbgyrH6FRLtEyIhApQoCpYeWCMY1lvng9gSPJ\nqr+rEh6lir2qYL1EeY0UBuM0Vw+PPdpYG6wThMrRjS2pWSzi6meatTjHecFOb7k3fPkw4qHN1cxh\nE+SJ49Ev/ZuFz1uhqfVkZ6G6bcy5R+i8+UHORTtIsVfa3tvcpGWOYD3EPPkEu2aTo70U+5VnS1Sw\nYthHXvkK7uJjpeODikKwnUFMM4RAFAZ6nsVtEfXvVSNwhWEWXyHKepV7OgS6RiscCk9p1ng7FZKf\n+Rra7SbZ4S5meFj0PTszXqiB8jnWBwUD2GwuOmgyNJLhzj5SCoIgIAwD2u0mWutx0ZYnikLy3NxG\nEVc13jDOdw5VFMH3GP4zINna2vop4FuAcGtr629funTpH9Ud8Do3zrdfrT0/+RT91BFKydoK8VU5\n7vyBpwrv2VuEzcHHFQMUYwqUipdaCKwOkRVlsAKPUSHapmglMA8/gX32UyRExBRFMWcHl3hp4xuJ\nIk1SMy9aJ/AyRPgMpQL8EuKRXqrYaARomXNUkbOdoBU6BhW9we3I18pFhhqybPmPlzlJIDSHSTkk\nnVtJNv4LlSXURWX4vILVYRKwFqY4v5yExXtJblcoL81g/aWP0xjtLHze5YDrQYxaknf2QtJ+9AHO\nnB0ixOI5AGRyXLWvheNMsMOZM+BPn2Y7OEF67t3kwxxz2CN48Qukc8a57mu8uB/z8HpKoOxKwhlb\noQY2QSyGXOBFpMtRNZSb1qulk5MJWuj8ePGbrz0AQqK0RrY3cXpc2OgsIjlEpH2kzVDOYPPRWONZ\nFCQ9MxXaznnSNCNNj8fVbjcJw4BGI2ZtTeOcJ8/zqYddFQq/GdyecX4jrF2Fu8FtfSdx6dKl/3ny\n/1tbWzHQXmaY4XVvnO9MWLt4cUPSNGcwWDKxrlgMCKXIzr+F6Mpni3Ccs/h571lKjAgITI2ntuzr\nzEwEcQSDh59C7VyFse2K7IizyZfZjd7CMlrHQR7Q1hmDfJWYAOyPAk53FN672rHViStMliHFjSs+\nKb6GJzGrf7dAOq73IrqRLfUxWy/pRIb9UWF0Q+VoR5bDUbnIqRkYXtiN6DTs8vwp8PJBRDNcXXEt\nneHxKx+q3Kbw5KcfQl25VLndC4l427t4sHXIKI1RNXSVjcF1ctUgmJNUFEJw2lzFdQNUK4NTsCte\n4itzx2dLCrmeP+jwyMZyOUDvPWltpMRzzr+EECBNWu01e0Fol/QmC4XKj0PsTseY1kmgwuBJhW9u\n4pubxRPtHJhRoeKlG4X+8wo458hzQ69XLAaUUoShJggCWq0GUoppCDzPC4N9Mzb3fqDvvFewquf+\nXsHW1tZfAL6NwnP+y5cuXfrXdfve98Z5mUG8XfrOyTmlLNjHhBD0eqObCHetDqP7kw/jbjyHzAaI\nPFs0zrC0eVM5Wx/azkdFr/TYN2q1BD13GtO/XgjeAxujy1xrPEYUScyUMcsRi4RYpoQiw/gA6TU7\ng9W0ngDbhxLrFd14kdc6DhzprKH1Hi2LPPFREpI7RZIX9y3SjkbgiJUjtfXGfoJCd1mSmCJ0Pru6\nHuaadpjTzwK08Cjp2Wga9oYakETKcm1fY51E+JzlMhsQaUeSrp5p37T77+nmu7Xb1Vp13tlJjXrb\nn+FCqyjmGnYv0NmfN6sFpIB+6zwbR19e2CbwZGvnaOy9AEB3+/Oll0TgSZaGrCXXezHrzbxSKxsg\nkIz7yRcwKpKPAAAgAElEQVTxoHwBJTzeOYKaxYWVupYnG8CGLVR2vEDIO2dmXvJyweLi8CWE1e2C\ndZg3+NZaRiPLaJSOT1mEwoNAT0Ph1tqxsS487Kq54Q2GsDuHe91znuDSpUu/Dvz6yh15HRjnZbh9\n6cfCc+50miRJRprW0wOWj7u5MHr28NuIvviHRRtVxUHK5jghkVUavkJgdVQd2vaeTMeEM153p6Pp\nywdY6xVV3I3RLg/Yr9BXF2joIZFIKitpAbrNHTI0XkhyF/Dc8PxCcVWkHDujwsMeZiGnOh4l8un9\n0MLjpMA5QWYkvVSOq4MNvXRiJIqrp0aSGkkncqRW0AmzWv8+lI69tKAkzazkRNvRnwtqCCEQOEZG\nkRvIjWCzlTNIFNeOCmpRKCqwT3XypZEC6S3PX5O86YKtZRsTzvLICx+oPQdAK7ILeWenAoK3vZNz\nzWNmMB8v73e2S/jW3QzfepAcEfeuknQL/eJQ2aUynACDRLM/CHj45LAyvF33jHfFPmuqMKrS5tWp\nGUAtodsESnScXoip1zy59p22d6sW8FWh8CAoPOs4juh223jvp2HwLCtC4W/knO8c3Io0y2sRbxjn\nW7TOUkparaKoptcb3lKf4k1fr9ElXz9PeHAF58UCh7EQAiND5G2EtkXFeNVai3wUE5iEZn7AOfsC\nB1IjBKgatq/cF9tD4bDeo5Rnq/0CXxmeJ3PHk/+8ENWNnoCxRrTAE2o946Efo+ozoFAoygqvPskj\nNhoZUrgFizDMyo/2Xl/QjmwpZJtZyVpsOEhCOrHl6qHm2lGEFnbhZT8aKcLA1eZa93tjeUVrqPOy\nL27/MY1kr3LbBF1/wLaOkDPkGPbJd/Jgs8yr3ZDL+6EbeQ1LGKCS8rk6178wNc5yxfOphOcgLVR4\nXt6PObeRLshK+oo0hSTjAX1t+jNN+vdzFWGCZtEJIALAobxFmYQgH6LnSESsbpTvTWOzpHx1twze\nrZ6zCG8bhuPou1KSMAwIgoBmM57WnrTbzWk4fNU1Xglp0v2O14rnfCt4XRvnW0Uch0RRwGiU0WxG\nd5VAwF58CpMcofIUH4aL7siy0La32LCJyoYL24Ksjw1j1EzYOzJDstMPErz8RQB8mtEc7pA1q0kZ\nEh8RyGOjrYTHY0FoHm1d4Vp6kv2xeEaVpvIE3Yalny4aslgX0pFVaEeeo+k5BfujiLUoQyk7nbi0\ndOyl5SIwj8B6UcHnLZGi8J7PdHKu9yKiAPppOQWRGkk3zhiYxVB+IB0vHhRjeu665OHzizlq4Qxv\nfum3au/FBEp4kpMP0bxW/Baj80/w2MYR8yuujjngKGgT5tX533ayTRZ2CLJFsYzo6ComaKDHnNPd\n7c9z4/FvL857+DzfsP1RGuYIgSvulzWFhyojXjjxDj4t3kqmWvTSgKjv2GjlpcmxKmf9UPAyWhTP\njHWF9z7SGwTi+DmSFMV1EocPGmRBgxESvCcyQ3RyiFcBzIS88/ap0nXulu7yK63QttYxGqUzoXDJ\nyZNFIdpsKHy20GwZu+EbKOMNz/l1ilmhiqOjId57Go3olieCW1n5CqnI3/ROwi/9IRaFmgvgaptj\npS4Z2VlYoSr9NwFYGZaOkzh83CTtnCTq7SBHfeI4Io06WBkWDNbjYefo6SQ7f16NIUdzId5hPehz\nPTnJ9VFjYd8JVM371IrcTEh77joVt+8wDdlspNMFS5XnBjDMFGtRRjIjh2mcpBsV3rPxkkBZ+pnm\nVCfnxlwL1Y1+wEbLlOQ0AUJlpuF868SYgao8/os7H6eZ1ueaZyHXNuAamKjD+Ue7CLFY0SyEIOmc\nJdx7tvIcQghG3XMEO4vGWQBJ5yztvaLPurP9Bc4ffJpH9/6YyBz3HE8MMxS3NnRDHr/+ER7jI6Sy\nxdX4TXw+eyd7fp0TnaLtTOJJ53LRHXlEWxSLCIskUQ0aKiGo4DqbT9UoitoCEzTIgyZCKoi6SJcj\nncVF3YVz3GncHYNf3N9+/3gBXYTCNXEc0um0AD8tNHvuuRfY3NwkDFcXYd4qrly5zC/90i+wtfUE\n29vbrK2t8cM//GN3/Dp3E/Y1UhB2K7jvjfOqPO/EYNa9fI1GRBjqY6GK4yNvOb91q61bIojIH3kH\n6spnKjYK3JyRnYVyWa3x1vkIL8q+mDQp5sQFgsEBwfCQfH2DMO0zbJ/BeLCocdG0JxT1OcEAQ+41\nLZXwcPMKaX6eg3QxPyrwtV51rXTjOKRdhb1RxMlWAvhKVagJEqMKvWhR9vSUKELWpzqGlw8Uw1wR\naTflwJ6MuipPOpij7HzumuSh825KXym94UH33MJxdWjFFgvor/sGWqpeJjIhZplpkkuIPv0Mh3SQ\n9njihd9ENY57oL334xD9IgQQuwEPDz/DheSL6Bs5CBi0ztHvXOQwPE2uGxy2HgQc5/V1BJCj6Aeb\ntE11yN15CJZ0CaCCaX+yExLb2lh4oe6W53x3vPHyOY9D4UXKQilJEAQI4fnpn/57PPfcc2xtvYWv\n/dqneOqpr+frv/4baTZXcK3fBI6ODnnf+76Lb/3W9wDwV/7Kf8HTT38LTzzxlld87q8W6hbkr2Xc\n98Z5FSYGc/7d01rRbMZYa6fecvm4SdjzVl7a2yA9aXTRF58kf+mZgnN4BtIV4cQqgyGEIA3aNNKD\nhW3K5mRxp9SOFeRDslaD4amHaV9/FpdbGuKQpLGJUwEaSypClHAkLib0Sa2er8aQ+wAtHG9eu8pn\n9h5gZMph5rqQdqRdpR4yjPueRyMeMV9m3Vynne2RyiapbLCnz/Cif4ITbUO+hPAktYr1OJ/SU0LR\nWtWNDPtJSGIUkbakRrHWzNk+Ko9lb6DZbJuxbGUR0n5uZ04H2QmUz8nHPWpvyp7hbLjHSGhUBef4\nPNbZ5+U3fxOPtpfrN5/Uh7W/P0C7dxmrosqWq3BQ9uJNrz81zt4X3OLLysIcEqkk4eTcHnTapyVf\n5tz2nwDw/Ol3kZx7jIiUnIB+sI70FlWzaMh8QMDNCYD8/+y9Waxl2Xnf91vDHs9wz7m35uqJ3RQv\nZ4otkqIkW7IGy3JsCIocAX4MbCD2i2Uj8UPy4glJHCMG4ofEMPJgBIgBx0HyYCSGHTiOoFgWY5Ki\nRFISVRKb7OqpqqvucOY9rrXysM94zz7nDnWL3TX8gQK6z93D2nuvvb/1fd//+38AroZ1/XgIYY+H\nZHaawTfGYqb39x/+w/+R0WjId75zh29/+1v803/6T3jnnXf4lV/58488lk984lMr/2+tJYo2R7w+\njHge1n4KsQg1L16UWaOKySSl2CA0fREBk4uKnnh7N0nKAh6+hV8uNa/AUXoxXlGvRCaxZH4TowKM\n8kAopMnxipM6yVU40VqHbLUpew1EOkH4beLkgFHzJoXTKGkrkphy5C5CmXwlZziDoPKgxybAk46P\nd+7z7aPblEtdkTaFtJsbQtqxHfKJ4TfoFvcqeUYH1hkicwAGrhdv81J2hz8qXkd4L+G2COFPClUZ\ntKWHkRqFlpbSSvaalffcTz3aUckgWX5NBG7J4/FEgalZDHzvnuSVWxZTWj6Vfh0tHcPGLTqjt9a2\nPYlCx0QvXAP73tbtGjLlXuM2nfE7tX+XzjDovEL7cD30HUwOIYwgrRZoxXBM8OILIAQZIaoYQ1aw\nUcrV82FZLKXRIm42ca5kGH0UbUt283vIwZisc7syzKJKx2yC74qNa1cHsLSvkx7o9fz/k+Q5n/eY\nzWaLH/3RH+fLX/6JSx3LMn7913+NL33px3j55Vce2zkeB54Twp5KLEKcy40q+v3t0psXYU5eZJ+Z\nRnfYvcnBJEeXExrJwTxcLZbY1I6qjCr1mhRehNUBwjk8t/ioWRqUdLHWkhcJjfGDueelygyCiOzK\nC0T338C0WgTZgHG4i/NW2yMqYbHKozRuXiO9OIcgoUEpPEoq3ekf6hzwnaNrgNwe0q4JT+2W7/O5\n9N/hLxUZSQED3aFbLjotNeyQHx7/Og/1Tb7Z+EkKWb/6r1jaOWlZ1XwrLEkmEcIQepakUESeISkU\nfs0bcjzxuN51jBJ452CDfKgVSFvwSvb7RK6aS2m4C2cwzr2rn0RoDaPtxhlANHdgg3GGzYsgAOUp\nzNS+lv0BtiixfkRQDBE4XBCAnC48yqJqvgLgB6jlxhp+AI2qzakQgsz5tMUAFLjBmH7nVaQAZx2+\nq69fzq0mElsY6Mpfbf/obwrnnjeadTo+LMb5ceMb3/g6v/3bX+dXf/U/+6CHcm7UfTeedDzzxnnm\nzcZxuNao4iz7PS7MwuplacjzEhBEcYskcfS8l5G2nP/DGdzcO14MavaZmhF1liGlpAjb9L2IePQA\nv5zg5yMyP0REDYzfwBqH0oJ4ckzZWQ8hSuEwygeToaeG2yIY08YJiRRVK0glBVIrPtLt8f3jXVph\nfZMLX1kmJyQ5Xyi+yyey31obP1TCHHW4Wt7jh7Ov8K3gy2Sy/iM+zjWetGS54F6/CucqaSkKx41O\nyW7seLevGGaaTlys5bHLUtDwct5MNlu/t+4bfiH8+vz/46aCesXNOXr6Kq/chsOxhO1CXADsiO2h\n72jwLqXw0G7dY3XFagi57PXQ14P5Yk1A1YAFqoYRYVytiqwFz8eVZbVNu7uy6LzKIT3RpeOOETg6\nx29wdP3TCOzGkPbpCk8nyrU2CIl8UCHoH9QxH1cp1W/+5m/wzW/+Nn/1r/51Dg8PuH//Hp/+9Jn6\nM3wo8Dzn/ATitPlfGeaIPC/O16jiIvnjM2JBQqvC6hUzHLxGG5P0yXBY5WFnpB7nEPMGh6sQQlAK\nD9+tM36VMxQ6YLxzCzM5IkqOqk49WpNfuY0eHoGOiYo+k2KP0lv3RKVw5DJE2gQBDF0LseSuaenm\nn/rYM3TDMVLVt19shnYpD+14pfhD9rPNrU8brJeKzeCM4UfTf8PXwp8mkevd2UorkdZwr78Yi7GS\nvWbOWwc+V1sFoa5yy6omuX48ctPGDJtV0j4nf5fQLfL6V6KUsfDxap7FfAy3X0NJw9VmxpCIiO0N\nNSIS7jdeYGfqPfdbLxNe260+Vs6hpKVXttDpADce0Rq+PS+hsmmK8D1cXhnu/HiA393ZeC7hLA5d\ndU2TEuH7DOMbtNQJwy8EoTYw/bkxvMew8/IKCe0kvFND2ot75lR9SPtx4UnJY18Uf/AH3+Fv/s3/\ngv39T/BX/spfIk1TfvmXf+WJMs7Pc85PEWaNKqRUZFlOmp6lH9ACjyr9WfdiLnvLg8G4dhu/exN3\nfJ982XUXAucUYhM7V1SNBOq8FmUNTgqyeLeSzszHWNVGhBHlUM9JQc3x+/Q6r9Qe3pOWQdlEIBD6\nRH2vgLyUeNO+yzdaE+726j+ss+t1zvGyfJvr+gA2qzgSkDGWLRq2plyozIi9MV+aGuiJXOU1R9rw\n5vseUrkVEY1hpvGU5eHQ40qzIPJKRrlmNy44WvKem57l3oPNX1efnC/p1YWFVtCLbnN1Us/cPohf\n4cUrVZRECMGRf4Pb+eksb9PocuxHxLtNXvDHwOoiU/seTX+IaIO7cRubl5SjCUV/gNAaMzXO5fER\nztxeWVwtwyk9L62CKu+chl1a9sHatmExpPBivGKCANrHb5LsvVR73HOHtL36aMiT1NrxwxTW/vjH\nP8G//tf/9oMexiPhacw5P33LjTPA9z3a7RhjLHleXOgluaj05yaPO4oCGo2QJEmZTNIVw7ycq5ZK\nE+7dRnurBs7hNmbahBAYqTBifS0mseAqGcS0sYeTmhnfybY7lFON5KAYo4vNnqoQgsTVfzQDbcin\nJUlSwPXmIl4rcATSEghDf6wYJ4JG9pBX1feJdEFOvZc9Q1rjFQN03TGlU0Qu4YvprxHYZQ/UcdCv\npEB3whOhXSu52q4WMYcjzeFxSdPLpwuh6sa0/Yxvfbfg4UDRierZxV/Wv0Uk1lcWplHvmVoE8Qs3\nVhd80an92CmFJrh5nVs3PK749ZGfNgOSYBeonpMKPIK9HZqvvkh08xrRS7cJbl7H22lTTuqfsYMq\nnL38/80Wu+KIhHB9ByGqlMcU8fjBRr3s00LaJzu5bQppPy58eIzz02eALgvGiQ/832XjmfKc6xpV\nhKF/KZ2pzr7f6ot5Fm/5JIQQNHaukGUZk3Ef6Sp1rJl3vCm8bZBYGSGlRCgP5XlgLbJIsaYEDOPW\ndXQyxJeggoAS0Kb6YIfZgJGO1pLt1gkyFyClo7QCLdcvQiszv/ZIl7R0Si/x6U0kxkpu7pQcJ4rr\n3iFfaP7BbNAciy7X3f2N90LVsMUBFIZj12ZPHBO5hNez/5evhj+DER6RNrw1qgzH8VgipVtJClTe\ns6MwglYs+f03BTsNw7V2zrsPBW8OlxTGcsPJ16grenxBf7N2XM2mhIfrvx/vfZIX26vXstuysFmF\nk1L6jG/sczOa8CB5gavJmxu3jV290ZWeQgZNKEuguZlBpj1EuQhfT7ovku69hJSOfhoS2RFlUrBD\nn4bpIwA/G2GFquans/jjQ7L29bVDbwtpA7hyiQjoBYTtNnleUparC6PH540+GSSzZxl2kzbCE4xn\nxjgHgUcY+rWNKn6QcrXLHvfJ3PK2fer6QAdBgO9fZTIZU6RjhLAYpypFr0pqAycUUnl4QYQfhLXH\nmemFG1Ny8N7blA50MUYKhw0i3KQKTep8ggpzjF71ZgdFPD9uZny0XPeQtHQkpSZQVTnWleaYNx6G\nzL7KhZN01IAfb/3uCivcaX+eu6xDi+FUQW39/pVWzmNDO/aYz2Vf4beDP8b7vUXoPSslN3ZKjpNF\nyLowkqvtgveONccTTTsu6I8lODgcrjLTH/QVN6+UDNLZq+T4Ge83UKJeTGMvyhjKEN8uwrgGxd6t\nJifbdLajkoeyS8cerx0nFSHm1ke5ElTHaXgZ5UTVqrdB1XTDaT01wiewbCSMwVq7Mk9KL16Jmtgg\nhhu3CafPqRFamsJBQwN7jO0uoihQ2RicJUyq8QfDh2Sta2T4OGQlJGIlDTZzPdzJkHbQQGtFFIUo\nJVdaNRpjHkse93GRzB5VEvQ5Fqhn3DzZeOqNc9U9KsI5V9uoojKW54/ubzKYZ9gTpRSNRnRmb3kb\nM1wIQaPRhEYTay3GGoq8xPM8ojigyMutHv5s0ZIkOUpJutdf4PDgiMn4gGY5QGFJ/Q5R3iMwCUmZ\nYZWe1xEnZVU/PYOnLGnpEep1i+pLM2/kEWjHS7sT3jpq0PAtZV7wUzvfWjMuzbDE5mLFYC9DCsfI\n69Iq1mnQsR2s/P818x6fLr/Bvxh/ceX33kQiTrSUHGZq7j1f2REMJtCfSF6+AXfvn5hDSxrIr8q7\nvKo2l0spCf3oNlfHi3aOD3Y/yWtB/Yd6EN6gM1k1zpkIKG+9RjdYLIIauuBecJsb+ZZSLQdoryqL\nWvm9InjNw9Z5ju3uzf9b2NVyvezWR2HpnYl1ziiPaKpkeo0CAh8X+BROYBodpMmxhWFoI0zYmu9b\nlAKUj3GSSBm0zauF4axE8MTcLWUwJ24KIeZ9lZvNGM/TOAetVmPervFx6t8/CqQUlOX5xva86cVm\nPPecn1BkWdWmrQ6PFp4+/1iEkESRf+aSrenZOEu+SUqJlBJPe3iewvd9yg0euZSCRiPEuUV3rVmI\nv9lqceQi0uEbhC4l85uEea/ynk1KWfgYT1Y6yTZEnmAzOwTGrkdIlXQkpSJQlRG4tZPw1lFEN875\nYe/bRHKdlOcpR48Ou6x7jzMUop4F3GLIxHWJxSLffDv/Lvv+Fe7kr85/SwvJjZ2C42SRI133nksG\nE0FR43jeP5bcvFIyTuFnvN/YOM4ZTKM952yVwuPG7ZiTXvP8Gtqak6T09ObHuBKuE6h245zjco+u\nXah/Oe2Rdm6gPA+nFEiNLXIYDvDHh8hiauCXJ3NZIJIxKE3uNdEuJ/W7aGkxzS62JheeOp9mDbPc\nE45SB0itkEHFsB+wMM5aGoQALSyFExQiqOqoBWhXoEyOoioFdFLDUtTGOUeWFfNImNaaTqc5VbgK\n2dlpYq1b6qt8/mYSj5Nk9mFdODyJeBoJYU+9cZ69nJtwUSN7XqM+yy0DTCbZOQzz5auR+b5HFNWH\n+GfYbWsOspsE2ZtoSpKgS5wd4xUJ1o8ZlT4D16iNHijpyKxPXGNsA1VirERJ8LXjpb2Ej4vv0tGb\ni3pT1YSa0O4Mnq1n+gpgaBvEatVofNS7SyZj3kxvzH8bpJUgyfJLPkg1vrbkpeTGrmQwcRyPJbf2\nCt47PHHd1vIF/W26ctVbr0O7sTjHwe4neXWD1wxwtZkx8DvEeSXD2ut8lKtR/fUGsoSW5mB0DYmj\n0yjpdV/D391ZCfrfz7s0XlGkE8OLkz9C9A8Q/UNEmkBRqYK5yZiic42gqJjwioxs9zbl3q36a/LS\n2np6gFJ607IzCMsRA3cVhCQvJbHe0LjFgZUBFh9UEwEEntxSuFbNd2sd43EC04WC1grP8/D9yrsG\nMTfUMy3rbXiSGODPMjbq8T/BeOqN82m4eI/Us9c5z+RAx+OUIPAusBi4nD6uVQh8lRC3vs3iv69c\nbTO816Zh+vSiK0TZMX4xJnVdYhLGNHEbFJiVcBRW4skTeuACMierbkPO8anGW+wV23sc+z6wpdKm\nKSaMadTmLmWNlnXTDfnJzreZHAY8KKq2mJNMcKtrORwvrqe0gpu7krsP4OFQ0goLhqlcCenOt51M\n+GTrjbXf67Abp/RlhHSGG7cCtpGNhBBMWreID3sk3g6djmKTlw1VWVveuc31eMw43kOFq8zm1GiC\nRjX+MFa8O7rB7V2F271eregGPdxkgMlKdJZQxC1MEJO3rzIIb9KlXvRES8vENGjWKKd4Npu/LRJH\nWI5Jvdapb49YImI5QJ1S21xn8MrSUJaGZLo+k1LOQ+HLeevl3PXyMR5XPfJz43y5eBpv5XPj/BjD\n2gsmdjnPLfu+5rwlEReZeCevy/c1URSQZcXGmu66/Hvj2osU9yYoZ+fesysM0pfsuUOO3BVsTYmW\nEJCVHp6/Tg4LVUlhJW0xxFflVsIXQCsoSJKgtjRpdrKhaNFw68Z5xx7hnFx5VjtyxKBs8HO7v83/\nefCjDExlwA6HrNU9Hw4hCiDJBNf3FMN3Hcdjxc3dgntHUyOnCn7llW+R9ptQniIBBkghGDVuUQQt\nXg1Of7hxU+MOBfb6S3hq8yrFIDkKb3FVJxTNLkfuCntyNWrQszs01OL6XKsN6ZQ+LgTsdLnb+gyt\n3XVDOBmy0ThXu7vadYbCUkgfz1bzLiqHJLqJL7dEtACztHiUQqBO4XhUBm/rJlhrSdOFroEQAs/T\nc8961lc5zyvv2lr7IfKcnz7v8LLwNMp3PhN1ztvegccV1o7jqm55MkmZTLIlgY2LhqgvNvlm3nIQ\n+IxGybnFVqRSmPZtdJHQC29WnKKyMhBaGDruCOHqPTlPVTrVJzHONV6ZEpIipKA8bY0oBAPR3T7O\nDbcnIKfv1hsrjjKPUBb8/O5v0ZgasKyUa3XLpRV04+q3g5Gk06wepDftqytw/NJLv0c3SBD+2VWr\nEr/Nzdvba7hnaHspBzc+TyfYbJhLNP3wJnveiInfoS+77IWryepeHtE4kS4OIsmDojP///vFLq1u\nfQ6/2agY95sQiay2lh5Wc4K+mZAkVfpjE04aYk+f1Y84n8Fzrkp7jUYTjo76PHhwyGAwmuetu902\nWit2dppEUYBS23p1nR3PPefLhbHiA/932XgmjPN2XEyGc5OR1VrRbleeWL8/XsstX8xTv6hIipiL\nrQyHk1PJMJuuKW7vgFQ4pRn6VwmL4XzF44uCjjuqXQEJAZlZ/dAfTEIaYkLXG8w3GnG62Ib1thu+\njhxuLKdI3fq+ciqI0dYJf+bKV+c576ORWqnTFjiyUhL5Jc4JulMu08M+3L4CP3Xje7zWrghYu62S\n0p3t413u3iTyzkZOmsgW4uqNjX83KIbRNTp6zLHcxW8GlZE88TAnqlH7gCdBtfAZmwA6OxtXj1IK\nHmSt2r8B845WdfBsNhcbEcAO661Ml3FyNnn69Pt6WQavKErG44Reb0CvN5yGvEt836PbbXPt2i6d\nTos4jvC8iwUfP0zynU8DnPvg/102noe1L+yVrhv15dzyeQhfp57pnGMUoqqhllKcySgvnYlNCxW/\ne4Oyf8Qovkazd4A1Dqmn6mEioymGJMSYE1Mq9g3j3KPhF6QZ3PYfEp2ogzba57Q2vs2gxOX1dmNo\nIw69m5goJHAplCXK5Fwt3sWjqNTBTnzbu6KHsy2EFDRVyn+w91X+9dHrPCw6dBtV3XM7LPnDtwyl\nEdzoGJp+yTjz6TZLjkeSl6P3+YndN+fH1ErwwO5xS63LWS4jMR7XX9tjcG9I29uSTJ9i1LxJO3Yk\nSUxUIyZy6N/kihoxIYJGg34Z0vYSlp/lg7RFq7O2KwBxSzE4jOgF12l42+dZ1FBYtxqpSAmq/s7C\nUUpNaiMCl6zMJAHk0ieYkvc6rs+xa25YCKwymdW0CuE0PM565CRJN+StmyilKIpiY95603HPs5C4\nODfm2cCHPay9v7//GvBfAt8AXgAO79y583e27fPcOF9QhnPZy1zOLZ+l1eT566PPPsbltpfOuXOV\njmwLuXtRA290RCY1g+AaskhBL+Q6tc1pakvhPBIX4ZaCMtZaAjOis8EQaQ9csT3c7+uqpKq75HG9\nb/YYNW/S3A2IpWA4UTT9xUGO8y7m4SHXynfIbYQvFwumQBQc5AGdsArzh7LgF3a/zq/1Psv94RWu\nNHN+/66bh6vu9xS7ccE4y/joLcfnou/xene9pjj1mlCjNb2Mt9Qr3A4V902Xtndv67bH6grtRvVg\n+o3bRKM/Wvn7gbzGFW+IRXIc3mZPT8itWLmZzoGMNkcehBS8o1/hemuLkPkUUQjvH7W4Hg0ZuDal\n30B4qyufsRP4ZGhToG2OXyZ4Npu3OQVQrsQzKYWuaaYi5Uq+2T+jd/p4ZDbXDf558tYVM7xcI18+\nDxoy+7EAACAASURBVGtfLp6AW7kL/C937tz55wD7+/u/v7+//y/u3LnzW5t2eOaN80UxW8nGcYDW\nlcrX42o1edaJNxvLzHPvdDZ3AboI/PZVdL/HJL5Kd/AmBQvj7JOR4uHLAs8V2GnfZoHD+o5oC91a\nSRiLZi3TdxmJatK1lXG+778MV6/QWnLh5IkcpudLvNtXeTjukD445uVwVTczKyTLUVhPGj7f/h5G\nvsu3jq5j7JWV7Qur2BHH/Jj3HfZa9d2iolhvbfU4MgFXX61y4GqnBdlm4+wA096FqQBLsyVIxgvv\nOSEiDi0IwbvyJbphSq9s0jpBwuvZNkG0edIluSLz21j3cGPufhnHrg26je+L2jiLxOKExHgBhoAs\naIEx6DJDlhmhS1GuJCxHa8b5JBFMCIE+c573g5HZnOWtl0s2Pa/yrMMwoN2u6q1nJVxVC9jnuEx8\n2Eup7ty587UTP0lOdqg5gWfCOJ9mEGd/P8/qSy/lwB53q8nTQlonWeEXxannCUKU9ihRJF4bad1c\ngEQKKI3A15WXr5bLfYTA2e3PIJcR2O3G2fMlJpG8E3+M6Mp6nroRWpLUIzqhThY0PB7uvsK9vuGm\ntyjbCuyEk7SLrhpidc7P3hjwmc57/NHxLoEqiXSJpuTjjXe2GrC9Zsmk5xHXKKQBvKNf4QWvOme7\no3Hvb54ND/0XaIXL4V3BuPsiHL1FRMI42GNXjnhbfQQbRmjRQ+vVSWydgGD7Iu1B0iSINL00Yjfa\n3qLynX6DsBNTuBR/A81eCoF1ErksYaoUpYopdJNcVQxoZe3ai6ekWvOazxrOfVxh7Yt4uLPyrFkf\nEaUUvl95141GtajtdForofDTxnERJcNnBU+A5zzH/v7+fwj8X3fu3PmDbds9E8b5dLhzvYQzDxUq\nQZFznemC7PBNmOlzX3aeexMarRbpYEwS7xGnx+AvFimakjqOoZKQlAGx2nyvhCe3tocECD3LXf8z\nNHc2G5vjNCBqrhuNbpxD+xXeeVvxgld50LuiR2b25u0soVKqencccqOZcC0cc+3m6mJnOA7Z2ZIn\nFlJwv+jwql7vbtEvI268tiBUBZ6gL7p03LrASonGb6+HfBsRJFde5uGgxPMV7/jXyP02N9RDDovW\nGqP7YdEm3uI1H098gmnIu19sN85v9VpErUoPPXcBsSu2zGVBaRVars5JT9m5hKtVCuschgAlHDiD\nO6Ga5Z+Zpf24QsWX440bY0gSQ5JkKCXZ3d0hSbJph7wqb12W5dwDP0ve+jLwta/9e37913+NbreL\nEIK/8Bf+k8d+zseBcwq/fWDY39//aeCngb922rbPl2IwfQlOt5hVSUXFxK7qls9P0rgsYodSkna7\ngRCCwWCdFX4RnIV4pj0frTRIRaZXW0QGpBtXsAXbvTdPWbIt+k/GCd7zP0Lqb2A1zcdX/3vDKxnk\nPurlF3mrqDojSeHoZ+vlTHm5+R70i/q2mCv7e/UtDe8FL6NPEK7Gfn2J2HvqxY0Or/A00c09wqs7\nuKiJ7zImNuBI7nHXvMC9ogrHGyfQ0fb7PjAtZnPfD/3a0jeAu702USuabyulJLWb+3I7JBZBWuqa\nObHkKWNwzlJYgROa3HmU+Fjh4/vn6xh3ljrn8+LxkcwcWZYzHI45POzx8OERo1HlZjcaEVevdtnb\n6xAEHl/96lc4ODi9fv68SNOUv//3/y6/+qv/KX/xL/4l3njjj/j617966ef5QcBa8YH/Ow37+/t/\nBvhTwF8Fbuzv7//Ytu2fe86czZs9mc9d3u8HFVKZnSsMfYLAYzLJtobDzj++s23YbsYcDYaUOqQw\nBk9UY1A4LHI1pD2FUqccWwgS0SRw62ph1sH3+Qh+FGLy7YuQdlSS5ZJAr48hywWqIRGvvMA7b1pe\n8B6uNHWYoak3e8Zan/4S7uyotWzSQdHi1kdqjHYQrkUMUhfQ2d38avbZYUcVOAfGgETwjvwIcVTd\nY0PA2xONtinNded7jsNJRBAsjLEQgsMk5gVvVWjknX6TuLVeIpXZgNJAy6+IUUnpcfeoxUHSYHmx\nm6YlN3cm7F8b4qkSgcE4iRJVhzKPAit8yukHzroqhB/oizWWuUz8oHo5b8pbp2nCv/pX/5JvfOO/\nIghCPvOZz/HZz/4wP/uzP0+7vV6/fx787u9+ixs3buJP6/M/85nP8ZWv/AZf+MKXHum4HwQ+7DLl\n+/v7PwL8M+DrwK8BDeB/AL6yaZ/nxpnt3uwy+/lkPnex3+MviXCu6mYVxwHGWAaDyRk+GrOIwNnG\nd9aQu6cVSnlYCoa2zS4LgyqsXStbgqojVV5qfLllMaF1rVrYm/Zl/J3KYxVK1jbVmEFKwVEWcUOv\n594bOgcEUgrkiy/y8O2MSA7hRG3ulXBCTnMapl/FlUa2saRrvk3b0e8F7HgLqzvofoRrNYNuN2Hc\ni+ZCKAAP/Be4uuHNHJQxO3F1Hcd5jLFgGlfxTjxiEzRJsnAjya60gkzEa6Ez54VYN5zn1XsTDy+u\nt/BVj/CAYSE5Gge8PwjJ3WokIssdTmgmWcBuKweCqnsajiIvsLZACYNzOeADVci7FcpzvyePy5Be\ndmvHs46zKEqU8vgbf+Pv4Jzjvffu861v/Q7f+tY3efnlV3j99S880jiOj4+I40UkqNFo8od/eOeR\njvlB4cPefXPKyj5d0GEJz4RxPu09qDOYVa1wiNbqlHzu+aU4LxrVbjRCkiQ7M9vzYp7z9sFV9aeO\nZuTTHxVIJRmXDRqiMoaeyzDUKF8JQeYC/C0FzUqz1h7yzeI2urvUxUgJepOAvcaW/PUGy70bpQzy\nBpFv0Z4kufEa4YPvkBSKyFs8X0HV6UrX6HIr4chUTGjX642Xr/VB2WHHex+AN7KbXP9ovRqYkIID\ndZ2GexOAiQvpdjd7jLkK8YWhtBJlS/Joh1Hh0wxX5+fxxEerkKxMCPT63D3OGsgaFrTSmvv9kFud\nlNIIxrTxtzDgCit5b9DkD972aUSCxlLU31pHaSoluZ/aX3jjUkqacfVuDQZjjLWUxuI70Eqh5cW0\nBz5MhLDLPqYQgpdeeoWXXnqFP/tnf+lSxtHt7jKZLObxeDyi292uxPdhxYfdc74InuecWTeYC5Uv\ntzWfe7Ea6fOxtaWUtFoxQghGo/ScZRjnZ4Zvg7VuqjVs8ZQA4SOF4YHZw7pqKnmUFLY+b+lOuVlS\nQiIXod+HXEV21nPMo+IUtbC4YFLU6H0D/clibGGsOOh+jH66npfdJEkKVU/h02D9ytvMraL5Sn0n\npxl0a2HRDoLbbBLDupfszI3wIA8YyRYon9BbnZ95KZBKIaTkvfHO2nHyUlKIeiUvgMRV43m738IP\nNpcxjTJFUmj+8F2fJLE8PDQMhouxpFn1fvzxj/Zqr2lmn5SUBJ4m8jWeEo8kVfuDqHN+9GN+OGqc\nP/3pz3L//j3yvEpLfPvb3+THfuyPfcCjuhiM+eD/XTaeCc/5dLhpqcJZveXpXhcihJ3dcw4CjzD0\nSZKcIPA4v27w+bz0TdvPvGVrXdXcYIqdhkdvWOArw7HrsicqGcuilHj++r3zVYm1q57xSZQ6gmJE\nnx0m8bXa+xtF2+tehRQMipDYWw/pnvTcGzs+mb6GK95aWcb4ZgKPoKO829UwgDf1a9xqbF8D77Rg\n0GughGO3W//AjBMEkQQsWakwBrymzyDXa15zbxLgT8VYpBdwnAR0o0Wk4SBtIf3NY4qaPm8cNGl3\n6xchzsEor7qr/f7dgPHYAtX7c9y3TBJHIxbkheXnPzPhWgeWVb9m783j8EifjJzzRQz+5dfxhmHI\nX//r/zn/4B/8t3Q6XV577YeeyHwzPFmlVGfFc+PMVEFJKtptnzw/e63wxQRFTjfoUop57+fhcIK1\nbtpq8nEX2q972tY6nLPUqZR5SuCEjxYlx2YH301oqQTf5WvHgeq6kjKgsaWzkpWCVMT0oluIDeHU\nwBccjn32GpubeIQbeiRfbUwYTUPbM+hYcy95mVv53cW1uYIJMUFNfVcocswG4tsMnabj7aNrXPvo\nGUg7QnAor6IDzZUN1/x+1mF3pzrfURKQejsErtL8XiFf5RLPWza8gl7emBvntFBwik55XggOsx3a\nG+qYR7mHlIK7DxRHPcvJZ53ljuGo4BdeL7i9a5kF6KRkusCDIPDJsur5XaY05ZPg5X5YPGeAL37x\ny3zxi1/+oIfxyHhSSqnOg2cirL3tPRCiCmPPaoWT5Dx1y5cbNgbwfY9WK6YoSkajZMXbOC/O+9Fb\nXmzMQtgVGWbzubvNBcnroblGbjWxnFDa+ql1agcqqXjPfwUht3uto2J7aDkOHA8G6+dSAvpjdeI3\nRx60OfBunhhr/RiEgFRu53ZYB8e7P3QmdjeA7Oyw26nftrCKZlx9fZJCkdiQZkPQTxTqhDEfpOvl\nR0IHTKYlUr2iiTxlThyNPWQYMkrXn2FaSJSCw6Hk7j2JW9M0dviq5M/9eM6nXlqPnnieZnd3B2MM\nWZajlEQpORWzqY51UcP1pBjSD5NxflpQfa8+2H+XjWfac54xsY2x5Hlx7lrhyxQUmbV2FEIwHCZr\nDNGLN+g4P7Z5yyfhKYFQPp4oKKTPu+YmL+p3yY1Cy/XlrKc2L3Fz63E3u4UUlq63fZEUx2orazvJ\nBe+NmgzznGZgCDxHy89RElo64+S6VGJI4iv0xzk7ZRWeV7bcuHy1UrPFceaB/yJWNIDtOtszDP2r\n2LLPDX+9W9OxadOOqpM9TGKIY4aJoNMwLC8Ox5nCrwlXCyE4SJrs2jFO+VuXk5NMYIRGIDhKQppL\nbSdLIyidIs0Vv/eGqPVWfuhmyc9/LqNOPj4IfBqNiNFoMi8ZqtJJs9rpyjDPDFfV7efsH70nxZA+\nN86Xjw87W/sieCaN88ncspQSfYGayouXRa3mnXxfE0UBWVZs6bf8+D3nGRqNkLKsVIrO0jhjr6nI\nioKi9DHC593iJjtqULutVo608Anl6nXODDNSU1rLaXJhvid4OAy50V4NkR+MQxIbgefTvg5FbjAN\nwQTopSV+1udWa8zItlbKugKZk4uYfnwTNS5pmj6hHeFkvTFTYvN96ekrmFaXHeew6eZe0/Pts4Cw\n5ZOkXXCrxjk1mmgq4TnONSPaXAksg0ytPdtx7uFv6CplRMRhqrZqbAOMcn8uE+mE5nDksdesaqon\nhQYh+b3vy1ot4xd2S37h8/XPbdYQot8fbp1Ty8YaNhvrTRUWl43HJ0JyPmvyvCPVdjyNYe1nzjh7\nXqVDvZxb9ryLMUSrXPVFXpoqHC5EJW6ilGQ0SrZ+tC5b9vMkqrCM5fi4j+d5eJ4miipPvtIJ3mys\nPa1oNySjXtXwoJAhA2MJ3KB2zLnzCFkY59T6vJPdBFlNRyEEhRErspp1yPFh2lDDWMHbww5+HK4E\nowcTR6tRHccPNYR7vG+a+DZbMc6eMKTTjmFHjRcxE81OeciYkLCmaUdATomHPpGXTWSDcesmTI3M\n0MTs6C1lV0Bf7hJKQRB73D/ucsNfyHn2XZudaSnU/XSHOBYcjhXd5upzOBwofH9zKiAtFc6FBFtK\n2YaJpHSrn4RRGVIOJFpanFC831MMT1AyrHV86iXDn/vjHkpVGu+zOWOto91uUJaWXq9+wbYN9cYa\nwK0Za3gyvFwpBWX53HO+TDyNgYhnxjhvZ2JflJBysZyzc9UiYeYtj8en9/S9yBjPatBn+WUhqg9e\nluVzso6Uctphp95Ya61pNCK0l3AwzMhslQvOZczdccC1sE+sV73kGdHLOMnDYpeBba+Qv4QQjHOf\nTrTde241JUkusU5wVHbx4/WSqKu7kqO+YXeposiogLH1EUYQL5HTpLMgqhKkQeMWdqKq0HbdPRSC\nRMa0bH/+U4nHUetllmO6hY6Bzca5X0SEzQVBKw27FGUfT1oS49GMqnn67qhVdeVSJepEaqA0YIW/\nIUNe4XisUdKx26w3zsbCMPdrrlUwKgKSrHoub7yZkhUO31coJSkLw/WdnJ/7rKHfT5m1T/Q8TavV\nQEo55S4YPE+f2uDhNMyqKpbz085V0Scp1xnhj47HwwB/HDnKZxnGfBju5+V6T8+EcRYC2u3GRib2\nRVddF/kACFH9C8PgVG959VwXGuHW8c1KpJyzG424tXajsZ511ymKEikEnUjw/nixYMltwNuT6zTU\nhOtRDymqpgcIOCzaHJsuTujacxfu9DImKQTvDFoEcYDe6DUKSicojVuptZVScFR0cK5HYyrXKV2J\nnZk4IRjF1xHjATGT2tdumdw2Uh36rVugVhcIVvtscVbpyy7B0g3wI807k5e5Ub7DkWmzJ0veHbc5\nZI+9OGeYKjonvOb+xD/B0F7FzCMujWOcChrh+mQaJApE/T3MchBC4omcnagk3IHQK+m2Ha+/alkq\n057LUFaNYQT9/nBusOM4RGtNWRqKopx72I/imc64GkEQMBiMUErO5zXMcpHuwsb6w5Nzfh7W3obn\nnvMTCufYKnf5qLnjs2JGQAMYj9MzG+bqXBfznDdh2Vs+D2YMbs/zSNOMJMnmxvrV200e/lE2V+sJ\nVElqfMamwfdGq7rSSpitYWshtst0AvTHkqHYIZDbPexOS5EbEMKglno++8rQsx2c6dNUCaHMGTl/\nwWYWAtPY4W7ZoV0c0LVHiCUvKlIFpVUcRS9SRO3aySC1JC80vli30PdGMcHeurcfxB7vTl7GSEE/\n9cmUh7aOw5FHagOGx4KGl7LbLBkmEnlK56beZPZ3wdHIoxGeyPeXkJR1XjNkRdXEQknHz358jP7U\n1lMhhKDVqp51rzeYv3PLHrPW1XwJw4Bms4G1Zt5i8TzGenYuIVbPtcz8PkkyO6+xfppFSJ4mfDg8\n58vFM2GcYVFfWYdH0bs+637LjTPC0H+s+eMZ6sa3SVDkrGg0InzfZzQazz+4y571bqQ4mKpwKQWu\n3CBs4raHC2eh7XZYT5BLc8lx0cLzFA8Hmpvd7eFSh+D+IMJZR+AZQs8SaIsUjoHdAQRNNUEYuyI+\nIgUU0qcf3WRgrtDIe4DACokVChPqLV47lQfumuyKdRZ2HnYJN0yEXhax01JIYDAQlE5iVYiaEr4m\ntkHRT1BKbi3X6o3lIhpA1ZzC2Hxl0TNIPKjpFewczGzqx64lnMaZ1FrRajXJsozJZHOqpiwrrzlJ\nFvt5niYIfJrNGOfcirGuI08ppabRsILxeHsP6stkhF8Gnhvny4d5CtMEz4xx3oZHIVudtp/WFQGt\nLBch9Yu2mpR19SnnwHlKpE5CKUWr1cAYs+KlnMS1luEoUXPvWQqLq6lHclRezLZLyqwG1o1zXkoe\nJM25NrT2NUlaEIXrFzXJFVmpeL/vkxXVyUxp6A8dO23Jrd2MK82CvmujhMEXOQWrjR7kdBHhlMco\nurp6AmvRNWNcRqnDtbKrNwdtomv17RwHiaTdrMY6SqCwUIpwReNaCMHDUcxeo2CT42wdDNMTfxSS\no6Hm6k5lddNckNn61EKaVx5ooA2vXdkenQjDgDgOGQ7H584rl6WZckCqcyhVGWvf92g0omqRUBTz\nMPiM5zAeT8iyeqGUbTgrI3z2t8vGeVtbXqZIy9OKLWq7TyyeG2cezXPelguKomAubnIZ/ZbPr0a2\nYJNX4eiLectRFBBFIeNxMveQt+Fmq+SdfvXB95QhN3UWWJIWEG9Q8oIqtF0YuVIbbSzcHzfnzG6o\n8uDvH0teubm4ttLApPAojOLdQzVfIIzHJWkGCMHRcYHWEQ8HAS/sphB32FNHVbOGJWfYEwWl8+oj\nAGfIBQpPU6QKT1RzoHQS1V7XvJ5hlPnsTD3koyEIzyfwV88znIBDcTCE215Ru8h5cCxWvOYZ+qk3\nN869iYeo2bnSC65WrZ+8sdkzFQKazYr41esNL6WDkzEGYwxpWhnrZZ5DHEdzUqIQEqUU5hGFjTcx\nwuM4WLmeyzKSVaj86fP0Pkg8D2s/wXgcpUibXlal5FzcZDAYr62SL+o5n58UUu1jreEiTTqkFDSb\nDYQQ5/rw7kSWB2MoDHjKkW0IbZs1dalVCCEY5T7dqAqRWgfvDVsrhnmGVifi+/dSXrxmsE6Slprc\nKN491MyUREajgiQT8wWLVJrhsKDV8nj7KGaUaUQHGmrM8r3W0jHJBcHJvoxU12Xd9lpmIQUj0aZL\nVSJ1JK7gh/Wh8N5YsdOsDnbQh8x47DRXrzfJquiBEAKk5kGv5Mbu6tjyAlLj10WrsWgGE4mWDiNU\n7axK84q5GOmS251671QpSavVpChKhsNh7TaXAWsrkaAw9ClLw3g8QWuF1h5hGExLk8y8guBRF8Kz\nXLZSck4ym5VvVeN5NEb487D25eNpvJ/PjHF+HKgz+GHoEwQek0m2Mbx3MU3u8+9TFIZm06fbbZ9a\nq3wSvu/RbMYkSUaSnKXUaxUvd3LeOPRxbA5tK3n6dZVLrO33Bk2crA8FA7Q7IQdjW+VJpeR4KAGJ\nMY5ev8Ah1+rSJ6mjNe1IeTz2sU7wcsfSUumKwd1ETBNCkJYesbc9vFqoEEzVEtIG0cZlVlp6eIHA\n2qo0a2dnVQe7KB2TVK14u5n1KcoMb+ltvt9TtR7xDL2xQkmHqGF5G1OZIeccX3y1RGu1ZvBmal9n\njaY8Cma57IqAOK1rN3Ye0l4u32o2Y5RSK2zw84TZpZTTumxDvz+cH3+5fGumEX5RRvh5jXN1zOdh\n7W147jk/xbhYp5zFy6iUJI5DrLVbmeGz/S72sp1tn9mHw5iS4+P8RK1ylU+dGeqThBshoNGo1JwG\ng9GFvRBfw7Vmyf2hJtQlSemtjV9KQVoIIn/zvZJSkhaK4yTAyu0NG4oSklyBEBweGByOJMmrFoqy\n3kNUStHv53Mj2BtrDg5DPvuqYi8czxcOnixxGyqJqwXEduMsPUVWehzLPfQGN/twqGhNO1hlRiG9\n1YXIJLGkhVwzulJKDgdi7j33RmxdxAAcjjSdpqvrvE0lUido+iU3u6B1jNYLg6eUQmt1qtrXZeAs\nuexZ+dZCEnTBCI/jaL64mM33sqxnhM9qsyeTdB5S34TLZISfBc9zztvxFDrOz43zDCclNc+6Dyy8\n5STJztRv+WKe89nC0nUlUttqleN4Yaxn3a/yvLiQmtNJ7DUsvQQyA1khCGrsRWkksH0BcG8Qo/zt\nU7U0MJkSmO6+XTBJLMY44oZ/qopbmsMsA3z/fkphFIWRfOFjjr2ptrQnDInVK6VYM5xJJE4I3nM3\niYN6b9Y50H61QDAWDsce48TR3akWjAfHDqH0RlJgZjycy3FumkdW2wc1GDpsCTevr/5ujMOhsM7x\n+RdHjMduNnx835/mfCtj0Ww2lkLJ5aV/ICvJT3XuXHZFIJt5zJWn7XkarSuZXK3Xy7eCwL8woQ3O\nzgh/HtJ+PHjci8QPAs+N8xSLVe7ZX5zZh1JrdQZvefVc52VeVwb9dEGRs5C+6ox1oxEThhpw+L63\npARWX8pyVrx2JecP3vfxlYEaz1NpttYz98eS44mmLVytcYepYU6rj+N7DwxVZY1EKpiMC5qt7R63\nUorhsCBJDMWUvHbQE9w/DvD2LG0/3bpwU6rydAO1eZGRFJq+axO6fq0xH+U+empQe6nHKFUYB/ce\nGKRSeP52T1gqxeFAkJcg1PbXejgqsU4ymEBzZGk1l0LkeTWGhszpxIsLnjGkk2TRuW2xwFuIiyyH\nki9qhJZDy73e5eSyZ2M6Wb4Vhv68LjvLCqSUc1WzR8EmRngUhY+FZPas43lY+wnGad+J874kQeAR\nhj7OwXicnNvjPv/7uPkEj1YiJaclUpWutnMOpeSJUpblutPi3NKD+9dyfu+ezzBXKyxoqFS+0lzS\nCNc/hv2J5DjxQQgmqaklZFkLk0yCgPsPCo77q3+XSpJlJUGwfaofHOQob3Wb3/++oNPyUdLS0Dm+\nLLAbXpnceBuNc2EEh2kbJxSDLKITrrKfjRUwbZGZFJK7D0Pm7bCExhjDdtNcoT9RKK1qSWAzOOcY\njhZplQdHEIUOrQVJarFoJonhpz69kByN45kC15iyXHiVJ/O5lyEucp7Q8qOgLA3W2mlf6YIkSWvL\nt2ZRgUf1zGaRBs/TaySzkxrhdd+h5wZ8O57GaMQzY5zPgrPMfykFcVypfA2HE1qtmPPr754/51xn\n0B9VUGSWzztJ6jHGYkw+75BVGWvvwsZaCPjMC4avfG/DtZ24MOcqwlI/XXi8pVWMk5JGtLrdKK1Y\ny/cf5Bz3LHU9HovC4fubF18H9weMJpbOboi/FD7PS8FXvq35kY/HXG0Kml7GsBD4uuZ6NzxO6+D9\n8Q5uanwnZUDLpivh8VFRec3Owd3DaO0aivL0xaMxjgdHsNuFcEur6/7ArJDzSiN4813H7etViiHJ\nLC2d0oo2K3BtwiZxkTCsxEWsdVNjV0wjMqvHi6KQMFxfBDwOaK1ptxsrkYDN5VvhSiSpIlWenYsh\nhKDdbmCto98fzKNgyySz5YYe8OiM8GcNzz3npxhnKVXyfY8o8knTfM4UvQiR7OKe82KnR/GWFx/d\ns5VIVcY6m3+4NhvrzR/dKAr42LWEr30/YKfpVsLYWkFeCHzPMcklRyNNaddD4JNM4mnLLMI7SqrQ\nobI5f/jdCY1YIaTCP+ElSylI05IoWvc/33+vT5JW482TfMU4Q5Ur/81vS37kE02uNuXGftRaQVpW\n5LeV449OMMyF5HASca1ZeabjXKGnXtT9QchgLNdERTxPMRyVtFv1r6tzjgeHJcYJhiNDuCGvba2j\nTkzLWMGbb5ckWZVe+KU/nU8Z0g2yrGAy2a7AtQkzcZGZ8VuIi/g0GgslsLIs8TwPKSX9/uCxN4U4\nC8lsPfUj8DwPrfW5yrdmSmZZlm9VTdvGCH8KncJLh3sCFML29/d/Dvhlqibv7s6dO3972/bPjfMU\n21aoM3F9IQTDYXIiZ3RRctfFPedHERSZlUil6XaJxW1YN9arH92Zh2RMRbRxrvK8dmNH5Hm8ddX2\nygAAIABJREFU81DTaVqa0SykJ8AJjseapFRsXCQJSW8MnYYhK6uewteaGa+/lPDN34OjocVTFs9f\n73VsTrTos9by/ntDsnzx+3hiiJsWuZYAF/z2HfjSpxu0/BRf57XPPLeacNrlwljBYdqkFOHadqUI\neTgR7EVjDD7SCd459rnf01Oq77pxFVJhrasltx0f5+RltZhJczZu1+sb6u6tc440qxZ/n3+1oN2s\njNdoNJkzoC8DJ8VFlJJLJLOqU1McR/O89eMg+VyUZGatWzHWZynfmr1rF72P1RyWiG15iucAPvyE\nsP39/Rj4R8Cn7ty5k+3v7//v+/v7P3vnzp1/s2mf58Z5ik1G1vf1vLXjLMy7ut8PJuw0O4+U1UQ8\nv7dclUjNcl6XoVg2w/pHt2qHOetaZYwlikKKouQnPjrhn/9Om+OR5ni0OIZzjiiE06IXQkgOBo4k\nhR+6nvH6SylSCv7yL4X81/9zSmHg/Xf7tLsxcWMRFpdKMugltDsRx4dj+v187VxCCCbDCc1Os+Ya\nHf/3vx3y8z/ZrkLTQUrDK1aeg5zWbU9Kn+OsubH0CqBwAXd7GiEVSS75ve+Bc4ZOWyBrjKtSgtF4\n3Xs+OMwZZ8vnEQzHhp0T2xWFZZLWz/E8rWrAfQ1/+ksennd+43URzObJLK2yuT3p+UPJJyGloNVq\nYq29FJLZevmWmIbxvXn5FlS68xeNrlWLtOc1zmfBE+A5/xhw986dOzMixb8D/gzw3DiflxAmhCCO\nA5SSp7Z2/EF4ztY6JpOMRiNCSjXP2+X56R+tWYiyKMpp7vB84z0voijA8zT9/pCyNCil8P1F7vFH\nXnV89bur+wghyAuL722/L6a05Lngix9J+NiNfO6dBEnK6x+1fOO7EqUkhw9GjEJNaydEAFoaBsOC\n3nE6bbpRf55x4ohb697z4YMRWWb4f/7dgJ/+iTZHkyYDaWgFKVI4rBPkBQxkQEXfOuU6LOTOx5WC\n775VebRCCHoDR+AVdLs1DPMlD8oYx/sPc3Ij1+Zfmjp2Wqu/HfVs7Zxz1lKYKqT6J1+XCHE5xus0\nVA1UPPr90Xz+biv5i6JgxVhX+e2zGeuFiMkiv3zZWOZhtFoNyhImkxSt1bSPvD4zQW5hmJ97zGfF\nE5BzvgYsv1iD6W8b8cwY59OwrENdkUCCaceb7aHfi8hqnicUvtxzOUkSkmQ1pFY1tF/2MIqVhUQc\nh9Pe0ZcboqzD8iLg+HhRJ22MIUkWucfXrijSLORbb68aMWslRenwNnRZMqXheqvgS68mKLn4wM8i\nAb/4E/Cdtx0TpyEtydKSLB2tHENIgb+pJovq3h4fjti71p7/NuoNybLKEBweGf79N8a8/rkWxil6\n6WorTGksgXdKDt/CpFAIBG05IU01SDUvv5mkhvG7KVf3NEG4eEW1lvQHBQI4HloQqt4TLgXjiaER\nV97baGQozYbFyLhESEm3JfjcRwpGo8fHkIYFOapKdQy3epN1ed8FI7zS816EkYtaYx2GVdj8ovXL\n50GdulhRFFsJcmVZcnBwyGAw5Nq1a88N8wXxYQ9rU+WZl5fM7elvG/HcOM/hpt5yiNbqVG95vtcp\n9cebznUWg76p5/JqSC2ZG+uKsLbwMLRW0xKp05m2j4oZ6essi4CyNOxfH9P2Ff/f95uUdok9XIBW\nq5EF5xwYw898fEQ7civlX8uRACUFv/jlkn/265ogUHODugxTlGwsmJ6iKKr7LqXk4P0+WbZ6795+\nNyfLBvz4j7YXvZ+nsMhpZKT+flsHWaloBZZPXR/ja4g9w7/8ho+eMt2q+Vdw70FJFJRoT2ItaGkZ\nTQxhHIDY0qaSqr67EVd56v5oE4vdgBBIAX/+TywWctsY1Y+Cs7aU3ARr6+f9LO9bRZQWnnUQ+Git\nfyAh+hn7e1sJ2CaC3G/91tf5e3/vv8HzfD73uR/mc597nddf/wIvvPDiYx3z04QnoJTqK8DL+/v7\nwTS0/RPAP9y2g9h2UQ8fDj/0V3webOtJH0X+Us3j2b2HKAqmK/yze6WV9xDT749r/35ZJVLG2LnM\n4Ca5zkdFlcurvMfhcHzuj7m18LXvR9w9CuYG2VmH71c53DSrWjb+ypdztCyRUpyq6fzf/28F9/ua\nYW+COllYDSgt0d72damnKhb8eLI5dHr9qubLX9hBnVDjctYR+WbNq3Wualjx8m7KzfaqF/fmfcc/\n/1o0H1eamo3pB98XeNt6SFN9rK7tCpKJYZLXX+twmCGl4lMvlfypz8/K5tTc4HmefuQa9xlmHuzj\njODM8r6+7xEEAUKwQtB6XJ7zo3rnFSkS3n77bX7nd36Hb37zG9y9e5d/9I/+MXrbR+sJwdWrrcee\nNP8Lf/vBB26r/vHfvLb1Ovf39/8k8B8BD4HiNLb2M2WclaoPJ8dxlSM1xjIana9sJIoqNnIdWWwb\nOp0mvd5o7fflEqnzohI6iFFKMhyO557/cu7O8zzgcj64j9ocYxlpAV/9XkxhBEo6fOUIPcte0/Dy\nFUccVx2IhBAYY8jzWShzXTYyLxx/958YJuN8rvi1DIHFj9ZZ1MtIhhOk1jXM7QrOOkye8ukfCvns\n5/dWvP/pBkT+YhFUGEFhFH/ik4LIWy/BaTZj/o/fLPnWXYX2FM45JpOyVknOWUuzvV31DMBkOTrw\nayM7aVJiLISe5S//Qrqxr/asbK7eWJ9toVcxpCsi4uP3YFebZCwvNGYqZqdpbJ8HjUaE53kXvrZn\ngfj1gzDO//Hfev8Dt1X/09+6fqnX+eQvyx4BWiviOKQsS8bjlDA8/YN3EpcVTXlUb7kK7TXIsozh\ncNUjP5m726QAlufFmZWcms3LZX6HHvzk/qT2b1qraVQjZzxO5nnHKArxvOUPbjV+3xP8tV+R/Hf/\nq0/Wy9cMrHMCa+pKpiqMB2P6B0PCRkCr21r7u3OOyWjCq7c1f/EXfYQY8V7f4+5xiJt9YIVkklfG\nLy0kDviRFwaUqSA1ev68ZkpRxhh+7vMp337DYGRFRNwEh9hYLjWDMZYHDzP+//bOPD6K+v7/r5m9\nd3MQUo4EBCtHOALhEuXyqBcq/QoiFASKIoKVKkqVby0eVXtQKyqUSwVRQKlULV7Ufvtt+dEvJcop\nEJVgggcJIERCNnvvzszvj9nPzOy9Mzu7Ccnn+Xjw0N2d7H4GNvOez/v9er/enboYYY7aZfO8gGBI\nFIhdP9SfMDCT94ntcY/vpBUdrEkNlpQfsg2ZlKXcwSZyMUvksZ1usCZeAYBsLKIWWl/WD77115xV\n026Ds81mgdlshMfjQzDIwWBgNbVEafHJjkYMzHzawy2iIcKo5ub0nJUSOYBZLEonp2DcC1buld+x\ntexoJ6p4Hs92exD3TPRj1V8CiNH0MQxYPgAYYnfPrvMuOM+5wDAMfG4/rA5rhK+1IAjwNntRaAMW\nzXJI35nSwiBKC4M47TSh2W+AycDDbBBgMXIotPEwsvLPk7qpxcLB4bBJN035+XlYMFnAS+95EeIt\nsFoNCPj5mHQPyzLweUOwO+LXzgVBQMN3HvA80Pi9B11KIm8wPG7RQ7pzfgC9S9T9A0Z/d+INUQmF\nQpI1ZrZtOAmkTTBVfTmxixmxHOUVArP4NXeDgUVBQV5KY5HECGJvPw3MupFt45qWoN0FZ4OBhcMh\n1mOdTrcUXLS5dmX+cxyn3VDEYDCE2zYyC5TxTEXk1id5d8EwDMxmU06U3ywrehET68hkv3zRuyMS\nLMp+6MDcSWa88HpjzJhFbwCwGXmpPUkQBDjPOeFx+qSAyzAMms+5UNSlg/Sc1+WFycDjl3MLYYhz\nU9a1IIiuKcZHAnKqN3LsohdGhsG9/2XAqx950RyygguFYDDFBuFkrSPfn/UgFDZdCQQEuF0BOPLM\n4ceiCMyAEKZeEUCmwSH+EBVRWCYIAux2MbsRr5NAD0T9hti/rGUHm0ikRW5Uo9P4RqMBeXl2uN0e\nVToTGQGCQNLYNDDrBd05X+CIoi8TPB5/HOGGNjMR7SYkQlhNzWkKzGrU0WqJbn0ymYxwOOxgWUah\naDcmrPlmSqa1bGWw7tkZGHKxH7sPc7AXyjtdlmXhcflgz7eDDwZw9tR58HECHs/xcDc2wVaQj4Av\nABPLY95kOzrkJxdkJUJUmudJN1TRCIIACCHMvJbH8282gzXb4n7HWJaFzxcKTxKTOX/OC78v8kLV\neM4Hm5UFazTC5+PAssC0cX6YjfoGB9HoxgaWZdHY2BROvSfuVc7UWCS6vqwH8VzMZKtaOxhGTOMD\njOrpVZFp7LZZX24pOB1NlVoL7So4c5yQcLSjln5lGfWGIi6XV1J5kp1pIJA62LGs2EYkCELKHaUe\nxAuUxAkpsuYbjNnBaiG6d1kPfjqxA/Z8egJnT7iR1yEPDCu2Owk8D5/LC78v+Zp9Xg5+7zmMrrDi\n7mnFmtdhsYgX+GRKc4KBZXHvJB5//LMHrMkCmz1WD8EHeSCcmRcEAY0NXng8oZhALghAfb0bVpsR\nXIjDneOBLh31DQ7kpiMYDKG5WfZaSORRnWmwJvXlbGdxSFZJFIxycLk8UiqczLZO5DGgpD0Iv1qS\nC6CVSjXtKjiL81rjv6Y9PZ1+nVgp+goEOAQC4gUr3WBHLkjKSTrZJJHoS04Fio+VNUej0aCpfSWy\ndzm5OYVaGIbBglmd8ZuVJ9HUEDlT0uEwAikGMvYsNeCeacUo6aReMCh/jh1mszHCESsVdiuLeycC\nz7/phcftR0GhDSbFYA6BYcGFOHCcgO/PeMEn6bnneQEN37nwk2vN6NFZ264/EeQGLp2bjmiPatlY\nxKQYKCF/d+LdoBGFdGRJIDuwrJg2VxqLcByX0sWsqcmJr7/+Gj17XgyWNYDWl7MLH6JpbUoU6aa1\nk02RSifYiZ/BqLq4a0VtLVsOwj7F+kWPYYNBGazjuziRm450Lu5aGdDbirt+0gmvvdWAoGIIhtsd\ngsEIyQAkmjHDHPjFXaVJ15+MaMWy2nuOTh1YzLnZiJffDeDs6WZYrEaYLUYIvHiTxzIC+CQe3iIC\nWD6Ie261oV9PdZ+fCrvdBovFpPl7GWksEj1QQukCFgwL/awQBO0KaTWQtLnXm1jUlsjFrL6+Dk88\n8RjOnj2L8vLBqKgYiiFDhmPgwHI6AjIL8ELbC87tqs+ZZZG0baSw0JEw7Z34PVnk5VnhdMZvA9Kr\nRUp0CoPCBSmYlq+2Wmw2C2w2/SYSMQxgNJpgNosXXOX6g8EQbDYrDAYDmptdWd8FGQwsmtxGPPZs\nDU6flXf0giDAYrOBUbQm8TyHm8Y6MP2/Okb0ykavP1mwJjtKPRTLX53ksOqtQNgXPOpzLMaEpioM\nBAzoKeCOCTbYrOYIFy0tNxvS+zKR5jPZSiuSYG2xmGA2i5kLZRpZzwEuSuK1ZalDFH41Njbi0KFD\n+PTTg/jss8N49NGn0LPnxXovt1WTiz7nifcea/FYtW11X13PkwZnBQUFDrhcHlV1XFFVbIfTGev2\nlYmhCEDqr2a4XPIFQrmzEGfgJvbVVoOsjmbCTl/ZCZTxL7bBsKmI/jcbhOjd+d93NuKN984hEJKH\n3ZssZrAGA0I+H66+zIa500sSrj9VsI5sb9PnnI7UhLDxb0FwfFRNGYDdYYmzIxNwzVAeVw+Td9aJ\n159+sJNnPWttJVKHsr4cDIYi1k9GNSrHNWYKSZtrvWEUL6lEjU13ybkIzrf8rLrFY9W7a8pocNYK\nw4guYYkoKLDD5fKpCkyJrDgzmblM0spEgJLs30hsbzJKIhuGYST3rHQdnPR0+koH5e5cvtiawsFC\nn5sNAhmVaTQaYy62HMdjy3sNaGgMwWpmYbMxuKjEgtHDCmC1plcfjL1ZYiFmSkS3uXT6ztVwtpHD\nmrcDOO+OUm8bWFhtck08FAzhisE8bhqdvE6uNljnSohFUAoE430XxMyM/P3RqnkQ3yvzbAAVfsWS\ni+A84e7PWzxWffDyABqctZIqOOfniylItQFBacWpNBTRAglcWuuvaq06iVBJzx1eIsjFj2ES+3Ar\n1bzkZoOsPRBQ5wuurJ27XPHLDnpCbnICgaC4E4/JbOiXGdjzWRAf7ArB5VOOOQWsNguC/gAu7sLj\n3ik21e+bLFgbjYaclSC0Bko5WIvffzFYp+4mkI1FgvB41Fn4EqjjV3xyEZxvmnOkxWPV9lcGUfvO\nbKG9Z1kk0RSpdFCmlTOZohPfqtMk2S0S9y+O42G1WjI2MEkXMt7S50s+kShWzatUw4rBJp0hHqRN\nLZsiMyWiMMocpWxXTk6S1ciZBmuGAa65vAOuG81i595G1HzLwWFnkG9n0KlDCH17xvfTTofIiWdy\nZsZuF3t8GYaBw2HPas3XYDCgoEBb2ly0E40nUIx0kFO6gJlM6avNE3wqdfxqYQTqENa2ySQ4sywD\njgtpasfKZlo5nvsXGQ0oYoDdbkMgII4JzEaQJrVzpzM9e1El8Ryo4vmCk4utIAiSZ3UuRgWKU7ny\npL7z6B1evGBHgnVsn2/qNH50P/GQvkYM6Zu9X2Oj0QCHwy6175H1G42iMU2kGj+UcRo/G2nzRA5y\npHURAPz+gPT7ry7rRR2/WgPZ7mBpCWhwVqCl15nnBbjdPjgcVrCsQ5WSWlkPzUWLlLjrsYFhGDQ2\nOsHzvKLHWhwEwHH6GYrEthFlHvlTZQbI1CqPx5d1YwKSDVBzU6UM1m53KlOOyGCdi5YzJaTEolQs\nx7vZIGlkh0Ns/VNmBtQEa1Jfznb/MlmbWPLg4PV6YTAo/bXTG4ZBHb9aD0KWb8JbgnYVnFNdq9Xs\nnJUtUj6fDz6fL6Jel5/vUKQwY+ulRqMR+flifTIXE3vI7jw6rZxOj7U8njH9mwcSSLI9+IBkBgBx\n7W63V/r8VEM8MsFut8JisWjKBiiJZ8oRL1gzDCO2guXAeINhIPUYp3KhEzMXwbClZaRAK91grawv\n621AEw+S7eA42VgEiB6GYYoJ1l6vD01NTcjPL8hZffn77xvw8strUFPzJdat2wgA8Pv9WLXqBXTq\n1BknTnyLmTPvQI8esQ3se/d+gp07d6CoqAgMw2DOnHlZXWtLwtOdc1snM0ORyF2FN+pCK9dLyW5D\n2SKVTdRYYiYyFIlMYSbu8Y3MBuQikIitbGIgkdPYsUM81O2Kkn2eHEj0yQYoiQ7W4qAFh/Q9KyzM\nB7F6TVeNrwal97ccuNInsuabOlgLghCuL2sXYqlB9uNO7LIXfcNK7Dprao7h3nvvRadOnTB48BAM\nHToCQ4YMQ3HxD7K23sOHP8XYsVfiyy+PSc9t3boFXbp0xYwZs1FbW4OlS5/G6tXrIn7O5/Ph2Wd/\nj02btsJsNmPJkoexb98ejBgxMmtrbUnoVKo2TqrrrFpDkegLrWgoYgfASEEsG7s6gqxW5jTvSCIv\ntNHuTZEpWBK4yDjJbEMutIFAIGaGNSF6iEf0rkhM48s3HMlQzszORX+vnDaXA0m8EY3pCOTSQY0N\nZ7okC9b5+eJNFcdxEAQhLNbK3s2qVmMREqwvuaQ3PvjgI9TU1OLgwQP4xz8+wvPP/xEvvLAavXv3\nycqar776Whw4sC/iucrKXZg/fwEAoFev3qip+RJutwsOR550TFXVYXTtWiJ5CQwaVIHKyl1tNzjT\nwRdtm2SzmTOduWy1WmC3R7ZIRe/q1AQKLZ+XKdGZARKszWYT7HYrGEb2RVY7sUctWqdyxe6K4il5\nY2vu5PO0O0apI1HaPJFALtNgLX5etNpcf0iwNoXHYJ4/3yxlmJQ7a6XITA8yr2eLwi+DwYCysgEo\nKxuAadNm6rI2tTQ2noPdbpceOxwONDY2RgTn2GPycOxYdU7XmUtoWruNk6jmnImhiNzbG9siFbur\nkwOFwWAEx6mv9yb7PL0hSmmr1QKO4+F2e6R5uGKgSN5jrYXI88t8KlcoJAaCxDV3LvydyM0UMGUv\neDppc3Vq9thgnet6b7zP4zjE3VlnMkgl2eeppbUJv4qKOsLjkfv23W43ioqKUhzjijmmLfF/745r\n+X8YnWl3wTmZIjv6NZLGFgQ+oxapVL29hPiBwhSuqab21CapwnQ/L1PipXlDIS5KSW2M6rGWMwNq\nL5S5SCsra+4kbc7zHAAGHToU6uJLnQjZFlN7/TW+mj1+sOY4Hvn59pzVe9Mx+kiWBlcbrMnnicr4\ntmMsMmrUWFRVHUZFxVDU1tagd+8+0q755Ml6lJZ2Q3n5YJw+fQqBQABmsxlHjhzCpElTWnjlFDW0\nK4cwQHQISxRojUYDrFYzXC5vRoYipJ5sMunnvJXYU1sM1jabJezl7Mlq3Y5ATDfUiNrIrtpsNsJo\nNEWJs5L3WJM0b65EdPHaiNL11dYCKUNk2xaTtJ5ZLGYYjQapVKFndiMecj3bA79f+/mla9dJ6vWZ\nlHVaQ2A+eHA/PvroQ3zySSUmTpyM6dPFVPrKlctRXFyM+vo6zJp1J3r06InGxkbceeftePPNbbBY\nLNi792Ps2PFPdOhQBKPR2GJq7Vw4hLVFaHBWIAZnC5xOl+Y0Ntn9BIMhuN2erDlvkTqd2Sz+AcR5\n1aStJVsXWZYV5y4LAo/mZnUTvKIh4ixiahGvx5o4pwHZnX5EENOgdjAMi+ZmV9K/x+RDSNJ3/8rL\ns8NoNMDpzN7AESXKwQ4AIuxSxWCtPbsRD7me7da9lz+eXad4U83C4/HA56OOXy0NDc7aoMFZgSCI\nwy+S9Scngzhv5WoogFL0FQyGIgZgZKO/12IRW6qy1btsNBql0ZIkWLMsC78/CLc7+97Y5MZKaxpU\n6f5lNit9weO7fynblnLh/U36e8WhHO64N44ku0H+ZFKKyNVYSSV5eWLGKhAIwmhUPwhDnihFHb/0\nggZnbdDgjNgWqcjhC/LwCJL+i/47k3eTQg53d8nHOxIluLibMGasBBd3d2KaPhdWeSRtHgoFwbKG\ntHqsMyEbaeVEQzwCgSAYBjn1/hZNb0RvczUWsfGDdeqbPj3qvWpQ3nhEt9UpsxvJgnVLjXo8deok\nFi78GTp37gIA8Hjc6NWrD5Ys+bV0zPbt72Pbtrel1qgJE27B+PE352yNmUCDszbaXXCOnumczsxl\nUqeTL1C8dJFlWTYnTliEdAdIRBO9K03X+SvXk52UXtXKG51szbFWumFlc441ICupbTYrDAY2qt6r\nv6EIgdx46NEGJt/0id+jeME6G/3SyZCNRdK78VB+j955521s27YNFRVDMXjwUAwaNARWqzXra1bS\n1HQex45V49JLLwMArF//IkaMuAwVFUOkY7Zvfx9Dhw5HSUlpTtemBzQ4a6NdB2etLVJGowFms2hk\nIfb2cuEUeHam9BDIAAlRZJbZRVaZfk2kBM+VSIkgDwBJ7N5EUPZYax0tSaYf5Xp3R+r10bO4o4d4\n6KEbyM8Xh4Bkq55N3LNIhka8yWXg9Xrh8wWynkXKdFCG3+/HZ59VYf/+/di/fz9qao6hrKw/nnnm\nedjtjiysODmBQABLljyMP/5xecTz27e/j+PHa9GxYzH8fh8mT56KgoLCnK9PCzQ4a6NdBmfxAqJ9\n5nJ0S0+8QEd2RHqkgEltkuM4uFyZibDiEW9XCiC8e82N+puYRGhVt8fOsVaaccQGOjJSMlc3HukM\nyYjN0Giv94pDR3JXz2YYhP3kRY2AvLPOzC41GWLpQ7SlzcRYRFlf9nq9OH68Fv37D0hoSJRNPvzw\nPRiNRtxww00Rz588WQ+bzY6ioiJUVu7Cn//8OpYvX5Pz9WmBBmdttLvgzDB8uG9ZvMNXixxE4get\nRKIgrV7I2XD6Sga58QiFxAtpOoEuE0i9XhQp6XfjwbJszK6UjMU0m81Z3U1Go9VdTGu9l/S7ezxe\njWpldchjLGMzENGKfJ7nFOWUkKZuBj2EZi1VX07FQw/dj6VLnwtnIeLj9/tx/fVX4F//2g2DwZDD\n1WmDBmdttEMTEvEXUvzlFEBqzalMRpS1V9G5KdH7R48EZKVgTUwg0mlVyaXTFyFRL3F8M5HMleAk\njZ2Nej3P8/D5AlJwMhgMYbW56L7FcRxsNktWdnQEZVuWFncxjuPAcZz0d0NSyNFDPJSzuGXbz+za\ncBJS1ZfjD5EwwWazxggV0wnWJCMQ70YgXeT+ZaLKbh0cOLAP5eWDpcDsdDbBYDDA4cjD2rUrMXfu\nPTAajairO4GSktILIjBTtNPugnPsLyRxAROkx8pdNcdx+P77BvTr11dTCjTR/GGr1SxdYJXBGsj9\ngAWl2jyeZaQ4ljEy0GXqCe5w2GE2G3MWREgPu2iCEYgJdHr6mgPR9ez4QznUIge6yCEeNpsFJpP4\n7ycIAtxuT07+Tm02q+QLkO7nJfI2t9msMJkSe5sDbcdYJBHvvvsOHnxwsfR48+ZXkZ9fiFmz7kDH\njsVYtmwpSkpKUVtbg0cffaoFV0rJBe0urZ0aQfpz8uRJ/O53T6GkpCsef/zXWTH2IBdY0TXLGBao\nIWcpST12r2qU4GIK1AGOS9xrqzdyG1ji2mS8c5B3peqCdaYiJbWQG4FQSLTklM8hcaDLBKXC3el0\n6Zp1UKbxlecgiufMaG7WfjPXmgNzW4amtbVBg3MCPvroQ6xc+TxmzpyNqVOnh0VSJAWurV6dDBK0\nBEFAKMSF7SFZXdqFEkEMG/R2bkqkBAcY2GyWnNXPMzH5IOdgMhlV9VincyOgJ8luBJQCOfkcQiBT\nn7Qgp5VDOTGGMZmMcDhsUgpX2xCMWOEXJXfQ4KyNdpjWTg3Hcais/A+ef341+vTpq3iFpMDl/wdS\n16tTkUj0pWwXstnEti09fJDTrZ9rhVw4PR75HOx2m9TbazabwDBQ5b6mFhK0tN4IRA5fUM6xtkfd\nNIUkJzNx98rnZJY1kHoMonKIh9KTmgQ7tUM89Egrq4FhGNjtNnAcj/Pnm6U1RE4NSx6sW3Ki1Lx5\nd0imIQaDIUZd7ff7sWrVC+jUqTNOnPgWM2fegR49euZ0jZTWC905Z4QcoMn/q9lVR/oroYB1AAAg\nAElEQVQ4p1YOK8cBarXozLX6O3r3Guu+pr8SXK5nZ8fNLFaRz4JhIE1byrZ4j2EYFBTI/dJa0srJ\nhnjEm3pG6suZpJXVkK6xiDLDQWZBf/DBBygq6oi+ffvBbLaipYRf69e/iLvump/w9U2bXgXLMpgx\nYzZqa2uwbNlSrF69LocrzA1056wNunPOiFhxmXihjC8uUyKLvgLweNITDMWKy+IJs+LXGBmGkXZ9\nuVJ/x9u98ryQdKRhJkpwsnsVd1r6ZwQISkW+IIi9tl5vAAYDi8LCfADZaz1T64aVCOU5AJHBWuxX\nZqT0t8lkAsMwaGrK/jxrQPZwT6dmH2+8ZH39SWzevAlfffUV+vcfiKFDh+OKK67GJZf0yvralRw/\nXoPNm1+F3+9H//4DMXr02IjXKyt3Yf78BQCAXr16o6bmS7jdLmn8I6V9Q4OzrkQHaz4mBR4M+rFx\n46sYOnQYLr98VEZCHY7j4PUq1buiqElMIcspP0HgYbPZ4PcHYnyHswERDBkMbMKUq3wO+ijBs9mW\nFQ9lr+35880RNxGkxzp6hnIib/Z00dOGM5rIYO0FwzCwWMyw28nOU4DDYZf+HbJVTycTrFJ9b+JB\nZkFPm3Y7pk2bCZfLg0OHDuLAgX3YufNfOQ/OM2bMxoAB5eA4Dj//+d2w2+0YMmSY9Hpj4znY7Xbp\nscPhQGNjIw3OFAA0OGeZSPHJV1/V4MknH0OPHj0wdep0BAKhjOvVSkIhIvQRa4xyP6kBgiDuUq1W\nS1bEZQS5hSiE5uZm1T+f+IbDmlAJLtdeXTkZykF2r4la3WJ7rOUZynl5dk3ZATJWMldZD6PRALvd\nKnUNKMsRNpsYsJXnkOmaiMMY6evXdgMTKfzKy8vDmDHjMGbMuIzWppUBA8oBiL8TgwcPxYED+yKC\nc1FRR3g8sqjO7XajqKgo5+uktE5ocM4Rn39ehcWLH8C8eQvw4x9PDAflSHGZnipwhmFhs1khCALO\nnWsCAKlWLV5c5dSrmJ7NPF2ZDS9u+YZDhNQY8/LsMBgMEAQhPInIk5PArGX3KmYH/AnNRJJlB2Sh\nGSeJorKNzWaB1WqN6F+OLkco7VLtdhvI5DYtqXx9jUVah+PXN998jSNHPsWECRMBAHV13+LKK38U\nYSwyatRYVFUdRkXFUNTW1qB37z5010yRoIKwHOHxuOFyuaSxcLEIiBaYaQ3W6QyQEFOv0T7Ocp1U\nTaxW1rOzPdmJQM7R7w8CEKImVambw50O2ZxeRYw4SK87KUfwvBDeveYmVQ/I/tjNzS5VAZZoB2KH\neIj/FomtRsUadyZ9/a3R8auh4SyWLfsDysr6we0WB9Xcd9+DWLv2T5KxiN/vw8qVy1FcXIz6+jrM\nmnVnm1RrU0GYNmhwbrUIiA7Y6QRrolRWO0AierpQMnFZ9M/l5+dushMgDzyIPsdsKcFl7+jc9fYS\nxywAETvSbCmllTt0PQZlxB/iEZnKJ1kIp1P7lDVqLNL6ocFZGzQ4XzCQnVr8/uqGhrPo1q0UJpMZ\nbnfmzlvxDSwi22xsNgtsttyNlEw06zkR0bs5LbXeTPul1aJsr3M6XSBZAbnliVXU3fWZeibvXrO3\nQ4+eA01wu70ayyqC5JNPA3PrhgZnbdDgfEEiB2hB4PHee+9g3bqXsXr1GvTocbHunxZvpCSpledq\npKQ8cjH1rOdEyAFCmR1IrARX+n/nwu3LYBBrr8myEMoeazFYMxHnoHad5AYrk92rGuQebfFGifxb\nqJtWRR2/LiRocNYGDc4XME6nE0uXPo1Tp+rx1FO/xUUX9Qi/oq+4TInRaJTcxeSRkvq0CiWCTFoS\n09j6BZBEnuDixCpreIxlbvy/U013SkTyVH7yujtpd1NbX9YKUfKLvf2RKnflaMlkAzBaatRjfX0d\nXnppNcrK+uHMmTMoLCzEnXfeHXHM9u3vY9u2tyVXsAkTbsH48TfnbI2tFRqctUHV2hcwe/d+jG7d\nuuPXv/6tdEEQUZqh6OcHnmgucWyrEB8RrLUi7rIcEATEnZaVKfGU4KQOCgDBoFgXjeeYpSeZtIIl\nUlEn67FW1pebmnKjACc3H4lKINHTqmQluBV/+9vfsGXLFgwdOgwVFcMxcOAgWCzWnKyb4HQ24dpr\nr8e4cVcBAGbOnIJRo8aiX7/+Ecc9+eTvUFJSmtO1UdomdOfcLohXr1ZrMyrOQRaVysm/FrG7oJAU\nINIVNBEHtUydsNSg3KFzHBeTytdbCa68+Uinhq6FaGEWCc4+XwAejzcrnxkNMRbRaqcaCARw+PBh\n7N+/D/v27cNXXx3HgAED8fjjT6O4+AdZWHFqbr99Mn7/+2Xo2fNi6bnt29/H8eO16NixGH6/D5Mn\nT0VBQWGLrK81QXfO2qDBud0R6wcOJB7eocds6XhTqshOLt7Fmvg4u1z6O2HFQ+n2lShI6q0ET2Vk\nkg1IVsDvD8JgYGNqvXr/XcvtZwycTq03H7HCL7fbhS+++ByDBg3O+Q4aAHbu3IGDB/fjgQceinj+\n5Ml62Gx2FBUVobJyF/7859djhl20R2hw1gYNzu2e+P3VoRCHt97aiiuvvBI9evTU7cIdOzSCidhV\nOxy2tHfoekBawcjQinRJp1UoEVarGXZ77uY9A7LDmNMZ2aMdPU9crxnQxFhEy7hOmdYn/DpwYB/+\n/e8duP/+X4BlE6/J7/fj+uuvwL/+tVsad9leocFZG7Tm3O6JHd7x3Xen8eSTj8Jut+OmmyaAzGLW\nA6WHs9st10jFerWYdvX7gzAajVkRlynJxNEs2vUrXU9wMu85VzacLMuEg2R8h7HEtV6bNOVJbY+1\nHq1Zrc3xCwB2796FQ4cOYuHCh/D99w04ffoUevToKTl+rV27EnPn3gOj0Yi6uhMoKSlt94GZoh26\nc6ZEcPTo51i8+EFMmTINM2bMhrw50FdcpoS08xDnLXknZ8pa2jXRTlIvYpXgHFiWAcfx4f7l7GM0\nGlFQoL39TJzyZJLOQyxJBJP2WOsxnKM1GoscPfoF7rtvHsrKRAGYz+fDrbdOwddfH5ccv7Zu3YKv\nvqpFSUkpamtrMGXKdJSXD2rhlbc8dOesDRqcKRHU19ehudmJfv0GxHlVXb06FbLQjEnYzhObdo0d\nfKGG6PnSuYDsJEmATjU7WQ+yMcEqXr+7cmdttYquZk6nS/MNT2sMzJTMoMFZG20+OPM8j/fe+yvW\nrVuLFSvW4JJLekuv/f3v23HsWDUMBhalpd0xceLkmJ93OpuwZs1KlJZ2Q13dt5g/fwE6dizO5Sm0\nYmKDdbq7aq21XtImRNyylMEhlQGH1l7iTCDiNmWPduIgp48SPNtZAYJSJGexiK18gUBA2lmr+2zq\n+NVWocFZG22+5lxTcwwDB5bDao1UdZ458x22bNmMDRteB8MwmDv3pxg+/FKFkYfIiy+uwogRI3HN\nNddh165/Y9WqF/DYY0/n8hRaMbH1arm/WnwcL1gTS0wttV6lUIkEObPZBJvNgsgxhpEK6lyPlVQO\nymhqckasJXp2cuQ4Rlv4PNUrwYm9Kc/zOZlgxfOicNBut8Lr9cHnC0g3HMoe61TDL1pS+LV37yfY\nuXMHioqKwDAM5syZF/G63+/HqlUvoFOnzjhx4lvMnHlHmxxOQWl9tPlb1L59+6FPn7KY5/fsqURZ\nWT8w4ZxsefkgfPzx7pjjKiv/I9WNBg+uwO7d/8nugi9oyMXVEP7DQhAMEATR7tPpbMbjjz+Kdete\nwvnzzRkrlUmQc7k8aGx0oqmpGcFgCGazCR06FKBDhwLk5dnRoUMBWJbF+fPNOQnMBgOLwsIC8DyP\npqbmlMGVGImI59EEp7MZoRAXcR7k5oJJUEMwGo0oLCxAIBBAc7M7G6cVg9lsQmFhHtxuLzweH3ie\nD5+HG+fONUkjJ81mM4qK5PMwmYzwhhVogoBwYM79jtnn8+HZZ3+P++9fhLvumo/a2i+xb9+eiGO2\nbt2CLl26YtasO/GTn8zA0qX0xpySG9rEznnRop/j3LlzMc/PnTsfY8deGfdnGhsbYbc7pMd2uwON\njbHv0dh4TjrObnegudmJUCgUYd5PSYR8sT169HM8/vgjGDNmLKZOnSGloLXWq+NBggNJWZMdOs+L\nNqNkZnCmbULJ0CN1rlYJno36ciqIsUiyTESi86ivr8PMmTNw0UU9MGTIMAwffikqKoZG/D7mgqqq\nw+jatURy1xs0qAKVlbswYsRI6ZjKyl2YP38BAKBXr96oqfkSbreLzl2mZJ02EWGee26l6p8pKipC\nXd0J6bHH40a3bhfFOa4jPB438vPzw/8toIFZJU5nEx56aCEWLfpv/OhH14afFdPfZICG3n7gylov\nCVhEQW232xSTtvQbxUhGWeqdOuc4Dl4vJymu5fOwSt9Fr9efE7cvQJ75fP58s6rPJOfRuXNXfPjh\n31FdXY29e/diy5bNePzxR7B48RJcd934LK48EvHG2y49djjycOxYdYpjHGhsbKTBmZJ12m2UGTly\nFN56aysEQQDDMKiqOoLJk38CAGhoaEB+fj4sFgtGjRqDqqoj6NKlKw4fPoTRo8e08MovPAoKCvHO\nOx9G+X9rq1enQjlyMbrWK3tp+8AwkOq8xMVKjbgs9jPFXZ/agKWFUCgEnudgMpkQCATh8/lhMok7\n9mwqwfXx5BaFX0ajGQMHVmDgwArcccdc+P3+nN/0ijfesmLf7XahqKgoxTHumGMolGzQ5oOz0+nE\nO+9shcvlwnvv/RXXXjse5eWD0LlzF0yfPhMrVjwHlmUxYcItkhhsxYplGDfuSlx33XjMn78Aa9b8\nCSdOfIOTJ+uxYMEDEe//8MMLpfoZANTW1mDbtr/BYrFEHHfbbT9G164lAIBOnTrjiSd+k+Uzb11E\nBuZ4JAvW6fVXk6lHosFJ8rqrICBClMUwjKQCt9nI4Iug5F6WKODKqvPYSUvZglh/Kn3Hg8EQPJ5I\nJbi4w9VHCU56pjOb+ZxY+BX9+5ILyssH4/TpUwgEAjCbzThy5BAmTZoCp7NJMhYZNWosqqoOo6Ji\nKGpra9C7dx+6a6bkhDbfSpVt/vnP/8E111wPQOwRfv3117B48ZKY49avfxF33TU/18trQ8Qb3iG/\neuzYUVx22Ui43V5dLDFZlpVmP8facwYhCJmpzrVCPjPd+rIenuDEbjRzY5Hcj3pMxd69H2PHjn+i\nQ4ciGI1GzJkzD6tXL5eMRfx+H1auXI7i4mLU19dh1qw7qVpbJbSVShs0OOvI8uXL8OMf3xLRS024\n//57cNllo+DxeHD55aMxaFBFC6ywrSAHaL/fixdeWIbPP/8MGza8BoMhO8kg0QxFDHBi+lX8fLfb\nA78/N4HZ4bBnbPKh1hNcVFebqLEIRTM0OGujzae19SAdNbjb7cJ3352OG5gB4J57fo4BA8rh8/kw\nZ84MPPPMC+jePVaARkkHMQVeX1+HJUsW4+KLf4g1a9aDZU2SwExvi1HiQe33B5CfnwdBEBAKhWC1\nWuFwOLLq+CWOlswLt2Y5kUlJO10luHhuFgBCRp/ZVgMzz/P41a8ewmefVeG++xbh+uvH43e/exLf\nfPM1nnzy9+jatWtLL5FygUN3zjrx5puvo3v3HhgzZlzKY5944hFcfvkY3HjjhBysrO3yxhsbYbFY\nceutU6L6f4WoP/r4gZM6brRXdTYdv+LVl7OJ0WiExWIKB2ZkYJfa+iZK6Y3P58Ntt03Ahg1voFOn\nzti48RWMHj0OvXv3aemltSrozlkbdOesAzzP45NPPsbUqbdHPHfmzBl07doV+/btQSgUwuWXjwYA\n1NXVobS0e0stt81w++0/TfBKtLiMj2jZAtQHa+Vwjui6a2rHL0ESlqmZtNUSNW2WZWCxmOFyueH3\nB6UbDjVK8NYyUWrFimWwWKyw2+2oqTmG++//BYqLfxBznFaxptVqxXXX3Yh3330Hd955N77++iv8\n9KdzdD0HSvuFBmcd2LXr3xgzZmzE7q229ks8/fTj2LjxTRQVdcQrr7yIY8eOoqHhLK666keoqBiS\n8P3Wr38RBw/ulx7Pnj0Hl156ecxx6XiDU4DInVtsfzWQ2AxFacN5/rwzLQEVcfwiJiSkziuOxbSD\n5/mIYB0PUuttampW1daVCaQ3nDh7AbJdajIluNfrRX39KXTu3BmRoq+W3TBZrTbMm3cvAGDz5lex\nceMrePDBxTHH3XjjBM1izUmTbsN9983HD3/YC6NG0TZLin7QtHYrJB1l95kz32Hx4gcjvMGfeOI3\nMd7glFREpr+V9eq6uhOoqfkSN988AW63fhOsyKQtMk6S4+TUMcfxKChwQBAENDe7M6ovq4EYizid\nrrR39iRDcOrUScydexcABsOGDcewYZdixIiR6NSpc3YXrYJNmzbA7Xbjnnt+HvNapmLNBx64Fw0N\nZ7FhwxuSIp4iQ9Pa2qA751bKa6+th8lkBs9zuO22aTGDOxJ5g9PgrJb4/dU7d+7As88uxaJFvwj3\nTOsvLiPt8XLq2AGDgQXP8/B6/WBZQ9a9wFlWFJtpMRYhGYKOHX+At97ahhMn6rB//3785z//xp/+\n9DzmzfsZJk68LUsrF0lHrNnc3Iw9ez7Gb3/7TNz3yFSsedNN/4Wvvz5OAzNFV2hwbiGSXVSuvvpa\nlJSUwmaz4Z13/oLnn38GjzzyeMRx6XqDU9TCYP36l7B9+/t45pkX0L9//4zr1akIBkNgWRYsK9Z6\nBUF0L7PZLGAYRtpVqx/DmBwiNhMnSmVmLMIwLHr0+CF69PghJk26DTzPJxzSoSeprHtdLheWLVuK\nRx55HAUFhXGPGTCgHIBYQ+7Tpy+OHDmUVnCur69Dt27dUV39BaZOna5+8RRKEmhwbiHS9QMfPvxS\nbNmyKeb5dL3BKeqxWq1Yt25THJtGdfXqdJHHWcr1ZdHlTDRDiR7DqAzWWq1C1ZqZxCOZ8ItlW16h\nff78eaxYsQwLFixEp06d8f/+3z9x1VXX6CbW/Mtf/ozz5xvRs+fF6NKFtk5R9IUG51bIqlXLsWDB\nQgDAiRPfols38WKhvKgk8waPR7aVq22JGTNmJ3glNgWeyfAOsX/ZAUFI7MkdPWmLiMusVjPy8hzg\neS4iWKeDHmIzOTC3vPArEYsWLQDHcXjyyUcBiNmlq666JiOxppIHHngom8untHOoIKwVsnbtSvh8\nPhQVFeH48Rrcddc96NGjJ778slq6qACiWvvo0S/AsiwuuqhHUrX2Sy+tjlCunj17Jq5yldqMZkJi\ncVk0xAc8U09uIi4zm0VxWbK+ZOWADlFspu3Xu60ai1CyAxWEaYMG53ZINpWrFCXx/MAF7NjxL7jd\nLtx662269y+bTEZpgAfLslIrFMdxyMuzw+8PwuPxpn6jBNDATFELDc7aoGntNkRrUK5SlET2V4dC\nQaxZsxK7d/8fli59Bn5/MON6dTQkGANyX7LVaoHJJNariclIukMvlOtv645fFEprggbnNkRLKlcp\nyREEYPHiRQAYvPjiaygoyEcm9er0PlOAwWCAwWBAU1MzeF6QdtYOhy3l0Avl2luD4xc156G0J2hw\nbidkW7lKSc3EibdhzJhxMBgM4WcSza8WH2carImxSFOT7GwWKS6LN/QiCL8/AK/XB7PZ3OqEXytX\nvpT09TNnvsOWLZsjzHmGD7+U9v9TLjhocG4n6Klc3bv3E+zcuQNFRUVgGAZz5syLeN3v92PVqhfQ\nqVNnnDjxLWbOvKPdz8BlGAZXXHFVsiOQOFir669mWQb5+XnguOTGIhzHwevlpCEeRqMRZrMRlZW7\nsWTJr1BePghDhw7HiBGXoW/ffoqbipaDmvNQ2gtUEEZRhc/nw+zZ07Bp01aYzWYsWfIwJk2aghEj\nRkrHbNr0KliWwYwZs1FbW4Nly5Zi9ep1LbjqtkA8cVnsUfIUq8jJWeoQ4HZ78Omnh7Bnzx7s378H\nDQ0N+MMfnsPgwem1GWklmW6itLR7hDlPdfUXMeY8mzZtwLlz57Bw4S8AiF0KAKROBUruoYIwbdCd\nM0UVVVWH0bVrCcxmMwBg0KAKVFbuigjOlZW7MH/+AgBAr169UVPzJdxuFxyOvBZZc9sg+fAOhhHw\nP//zd3z++Wd4+OH/1mwsQoRfdns+Ro++AqNHXwEAaGw8h7y8/IzOIB2oOQ+FIkJllxRVNDaeg91u\nlx47HHlobGxMcYwj5hhKJhDFNAvAgFBIwIoVK/DKK+tx661TEAiEINeu00cQEFZkx7ZKFRV1bHHv\n6FWrlkv/H23Oc/r0aQDAyJGjUF19VBK3VVUdkTQUFMqFBN05U1RRVNQRHo88ocntdsXYXMYe445j\nhUnRi6effhxOpzOsAi+Alnp1axN+xcNgMOCFF56VzHkWLfpvAJHjWTt37oLp02dixYrnwLIsJky4\nhdabKRckNDhTVFFePhinT59CIBCA2WzGkSOHMGnSFDidTTAYDHA48jBq1FhUVR1GRcVQ1NbWoHfv\nPjSlnUVuv302evXqDaOR/DpHB1g+6fCOC8VYJJ5pDgD06VMmueYBwA033IQbbrgpV8uiULICFYRR\nVLN378fYseOf6NChCEajEXPmzMPq1cuRn1+IWbPugN/vw8qVy1FcXIz6+jrMmnVnUrV2fX0dXnpp\nNcrK+uHMmTMoLCzEnXfeHXHM9u3vY9u2t6Va94QJt2D8+Juzep5tk8h2LRFqLELJHlQQpg0anCkt\nzhdffIaGhrMYN+4qAMDMmVPw6KNPoV+//tIx27e/j6FDh6OkpLSFVkmhULRAg7M2aFqb0uL07z8w\n4jHP87DZbDHHvf32VnTsWAy/34fJk6cmdDmjXDg8/PBCeL2y13dtbQ22bfsbLBZLxHF0WhqlvUGD\nM6VVsXPnDowcOQo9e14c8fyQIcMwatRYFBUVobJyFx577JdYvnxNyyySohvjx9+Ma665HoBY3nj9\n9ddiAjMA3HjjBDotjdKuoIUmSlq8/PIaXHnlZXjjjY347LMqTJs2Ca+9tl7XzzhwYB8OHtyH++9f\nFPNaaWk3SfE9bNil+PTTA+A4LuY4yoUFCcwA8NZbb+K22+LPJD906CBef/01vPzyGhw5cihXy6NQ\nWgy6c6akxd13/wyhUAjHjlWjX78BuPXWqZg6dbpu77979y4cOnQQCxc+hO+/b8Dp06fQo0dPSQG+\ndu1KzJ17D4xGI+rqTqCkpLRV2ElSUpPOtDS324XvvjuNSy7pHfc96LQ0SnuDCsIoaRMMBjF37iwU\nF3fCsmUrJP/iTDl69Avcd988lJWJAjCfz4dbb52Cr78+LinAt27dgq++qkVJSSlqa2swZcp0lJcP\nSvne8+bdISm8DQZDTCqc+oC3Dt5883V0794DY8aMS3nsE088gssvH4Mbb5yQg5VRMoUKwrRBd86U\ntDGZTOjffyA+/ng3GhvPoWPHYl3et1+//vjHP/4v6TFad+mXXTYqaa1y69Yt6NKlq+QDvnTp09QH\nPMfwPI9PPvkYU6feHvEcnZZGac/QmjMlbT766EOMGTMOkydPxR/+cGGoZY8fr8Hmza9i/foXsXv3\nrpjXKyt3obx8MIBIH3BK7ti1698YM2ZsRCamtvZLLF68EIDoOPf++3/Fxo2v4Lnn/pBwWhqF0pag\nO2dKWmzdugVvv/0mfvWrX6O0tDvWrVuLJ574FX75y8fitj21FmbMmI0BA8rBcRx+/vO7YbfbMWTI\nMOn1RD7g1NEsd8Qbpal0/erVqzd++9s/5nhVFErLQoMzJS2mTp0ekVq+5prrWnA16TNgQDkAsd48\nePBQHDiwLyI4Ux9wCoXSGqFpbUqb5ZtvvsYHH2yTHtfVfYvu3S+C09kkpa6JDzgA6gNOoVBaDVSt\nTWmzNDScxbJlf0BZWT+43W6EQiHcd9+DWLv2T5p9wAHg1KmTWLjwZ+jcuQsAcWZwr159sGTJr6Vj\n2osXOM/zeO+9v2LdurVYsWJNRCvU3/++HceOVcNgYFFa2h0TJ06O+Xmnswlr1qxEaWk31NV9i/nz\nF+gmNKS0DqhaWxs0OFMoKmlqOo9jx6px6aWXAQDWr38RI0ZcFiFSai9e4MeOHQXDMHjkkYfwzDPP\nS8H5zJnvsHjxg9iw4XUwDIO5c3+KJ574Tcz4xj/+8XcYNuxSXHPNddi169/YseMfeOyxp1viVChZ\nggZnbdC0NoWiksLCDlJgDgQCOHr087jq4bff3oo33tiEDRtehtPZlOtl5oS+ffuhT5+ymOf37KlE\nWVk/SYFdXj4IH3+8O+a4ysr/SP3qgwdXYPfu/2R3wRTKBQIVhFEoGfCPf3yEa6+9Ieb5tuQFno7D\nVzSNjY2w2x3SY7vdgcbG2PcQ1fIO6ZjmZidCoZBiNjWF0j6hvwEUSgbs2PG/WLr0uZjnS0u7Sf8/\nbNil+OUvfwGO4y5Iy9Hnnlup+meKiopQV3dCeuzxuNGtW6zdpqiWdyM/Pz/83wIamCkU0LQ2haKZ\nAwf2obx8sBRMlCrwtWtXIhQKAUC79AIfOXIUqquPgmhaqqqOSA5fDQ0N8Pv9AIBRo8agquoIAODw\n4UMYPXpMyyyYQmll0FtUCkUj7777Dh58cLH0ePPmVyUVeMeOxVi2bKnkBf7oo0/FfY/vv2/Ayy+v\nQU3Nl1i3biOA9P2+9+79BDt37kBRUREYhsGcOfOyc6JJcDqdeOedrXC5XHjvvb/i2mvHo7x8EDp3\n7oLp02dixYrnwLIsJky4RRKDrVixDOPGXYnrrhuP+fMXYM2aP+HEiW9w8mQ9Fix4IOfnQKG0Rqha\nm0JpQXbs+F+YTGZs2PAy1q/fBADYtOlVsCwj+X0vW7Y0xu/b5/Nh9uxp2LRpK8xmM5YseRiTJk3B\niBEjW+I0KJSEULW2Nmham0JpQa6++toI+1AgPb/vqqrD6Nq1ROqjHjSoApWVsd7hFArlwiTpzplC\noWSfsrKyqwA8W11dPSL8uBrAT6qrqz8NP64DcFV1dXWN4memh4+ZGH48N3zMzC0Y/9gAAACvSURB\nVFyvn0Kh6A/dOVMorY8zAPIVjwvCz6k9hkKhXKDQ4EyhtD4+BDAKAMrKygYBOFRdXe0MP/5h+JhK\nAD3Lysos4cdjwj9HoVDaADStTaG0IGVlZVcC+CmA8QDWAFgWfulZAKcA9Abwu+rq6mNlZWWdAHwK\noFd1dbWvrKzsOgC3ATgLIFhdXf1kzk+AQqFkBRqcKRQKhUJpZdC0NoVCoVAorQwanCkUCoVCaWX8\nf+WycGmQdQQaAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c1b8db2b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(9, 6))\n",
    "ax = fig.gca(projection='3d')\n",
    "surf = ax.plot_surface(X, Y, Z, rstride=2, cstride=2, cmap=mpl.cm.coolwarm,\n",
    "        linewidth=0.5, antialiased=True)\n",
    "ax.set_xlabel('x')\n",
    "ax.set_ylabel('y')\n",
    "ax.set_zlabel('f(x, y)')\n",
    "fig.colorbar(surf, shrink=0.5, aspect=5)\n",
    "# tag: opt_plot_3d\n",
    "# title: Function to minimize with two parameters\n",
    "# size: 60"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "uuid": "72b2e44d-2127-412e-9046-2b0c7c5bf7c6"
   },
   "outputs": [],
   "source": [
    "import scipy.optimize as spo"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Global Optimization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "uuid": "e6c829bb-f358-430d-9e8c-781e9d15c9e6"
   },
   "outputs": [],
   "source": [
    "def fo(p):\n",
    "    x, y = p\n",
    "    z = np.sin(x) + 0.05 * x ** 2 + np.sin(y) + 0.05 * y ** 2\n",
    "    if output == True:\n",
    "        print('%8.4f %8.4f %8.4f' % (x, y, z))\n",
    "    return z"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "uuid": "d1f54d32-6cb5-4cd2-8a95-ea3b92c87266"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-10.0000 -10.0000  11.0880\n",
      "-10.0000 -10.0000  11.0880\n",
      "-10.0000  -5.0000   7.7529\n",
      "-10.0000   0.0000   5.5440\n",
      "-10.0000   5.0000   5.8351\n",
      "-10.0000  10.0000  10.0000\n",
      " -5.0000 -10.0000   7.7529\n",
      " -5.0000  -5.0000   4.4178\n",
      " -5.0000   0.0000   2.2089\n",
      " -5.0000   5.0000   2.5000\n",
      " -5.0000  10.0000   6.6649\n",
      "  0.0000 -10.0000   5.5440\n",
      "  0.0000  -5.0000   2.2089\n",
      "  0.0000   0.0000   0.0000\n",
      "  0.0000   5.0000   0.2911\n",
      "  0.0000  10.0000   4.4560\n",
      "  5.0000 -10.0000   5.8351\n",
      "  5.0000  -5.0000   2.5000\n",
      "  5.0000   0.0000   0.2911\n",
      "  5.0000   5.0000   0.5822\n",
      "  5.0000  10.0000   4.7471\n",
      " 10.0000 -10.0000  10.0000\n",
      " 10.0000  -5.0000   6.6649\n",
      " 10.0000   0.0000   4.4560\n",
      " 10.0000   5.0000   4.7471\n",
      " 10.0000  10.0000   8.9120\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([ 0.,  0.])"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "output = True\n",
    "spo.brute(fo, ((-10, 10.1, 5), (-10, 10.1, 5)), finish=None)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {
    "uuid": "dc42167b-4e8f-462c-8aad-a94afdf0a8bc"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-1.4, -1.4])"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "output = False\n",
    "opt1 = spo.brute(fo, ((-10, 10.1, 0.1), (-10, 10.1, 0.1)), finish=None)\n",
    "opt1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {
    "uuid": "ec2669cd-36a5-4b79-a90c-761a39b12044"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-1.7748994599769203"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fm(opt1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Local Optimization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {
    "uuid": "e451a278-e2ae-4d86-b357-f230468052a4"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " -1.4000  -1.4000  -1.7749\n",
      " -1.4700  -1.4000  -1.7743\n",
      " -1.4000  -1.4700  -1.7743\n",
      " -1.3300  -1.4700  -1.7696\n",
      " -1.4350  -1.4175  -1.7756\n",
      " -1.4350  -1.3475  -1.7722\n",
      " -1.4088  -1.4394  -1.7755\n",
      " -1.4438  -1.4569  -1.7751\n",
      " -1.4328  -1.4427  -1.7756\n",
      " -1.4591  -1.4208  -1.7752\n",
      " -1.4213  -1.4347  -1.7757\n",
      " -1.4235  -1.4096  -1.7755\n",
      " -1.4305  -1.4344  -1.7757\n",
      " -1.4168  -1.4516  -1.7753\n",
      " -1.4305  -1.4260  -1.7757\n",
      " -1.4396  -1.4257  -1.7756\n",
      " -1.4259  -1.4325  -1.7757\n",
      " -1.4259  -1.4241  -1.7757\n",
      " -1.4304  -1.4177  -1.7757\n",
      " -1.4270  -1.4288  -1.7757\n",
      "Warning: Maximum number of function evaluations has been exceeded.\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([-1.42702972, -1.42876755])"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "output = True\n",
    "opt2 = spo.fmin(fo, opt1, xtol=0.001, ftol=0.001, maxiter=15, maxfun=20)\n",
    "opt2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {
    "uuid": "0352d556-6ea7-47a6-9c76-e4a56c0efed7"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-1.7757246992239009"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fm(opt2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {
    "uuid": "ff9beaf9-73d7-4157-85cb-24783abae775"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization terminated successfully.\n",
      "         Current function value: 0.015826\n",
      "         Iterations: 46\n",
      "         Function evaluations: 86\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([ 4.2710728 ,  4.27106945])"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "output = False\n",
    "spo.fmin(fo, (2.0, 2.0), maxiter=250)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Constrained Optimization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {
    "uuid": "703a8ac0-1c74-4851-9fd3-7ac404ee3446"
   },
   "outputs": [],
   "source": [
    "# function to be minimized\n",
    "from math import sqrt\n",
    "def Eu(p):\n",
    "    s, b = p\n",
    "    return -(0.5 * sqrt(s * 15 + b * 5) + 0.5 * sqrt(s * 5 + b * 12))\n",
    "\n",
    "# constraints\n",
    "cons = ({'type': 'ineq', 'fun': lambda p: 100 - p[0] * 10 - p[1] * 10})\n",
    "  # budget constraint\n",
    "bnds = ((0, 1000), (0, 1000))  # uppper bounds large enough"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {
    "uuid": "8f989832-637a-4188-b096-26ceeabd77ea"
   },
   "outputs": [],
   "source": [
    "result = spo.minimize(Eu, [5, 5], method='SLSQP',\n",
    "                       bounds=bnds, constraints=cons)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {
    "uuid": "67c11995-124c-4f9d-8edf-1364b412e754"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "     fun: -9.700883611487832\n",
       "     jac: array([-0.48508096, -0.48489535])\n",
       " message: 'Optimization terminated successfully.'\n",
       "    nfev: 21\n",
       "     nit: 5\n",
       "    njev: 5\n",
       "  status: 0\n",
       " success: True\n",
       "       x: array([ 8.02547122,  1.97452878])"
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "result"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {
    "uuid": "53899a89-8532-4f22-a17f-54d106412867"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 8.02547122,  1.97452878])"
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "result['x']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {
    "uuid": "b8548809-fe3a-4fa4-9496-8d3b6a177973"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "9.700883611487832"
      ]
     },
     "execution_count": 70,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "-result['fun']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {
    "uuid": "7453e87b-a70d-47b9-8a12-c5c0f01e4b86"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "99.999999999999986"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.dot(result['x'], [10, 10])"
   ]
  }
 ],
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